[anki:play:a:0]
“to speak away”, originally meant to “disown and disinherit one’s children.”
Anki
Master Deck
Here is my growing Anki deck that I use to memorize ever more useless facts.
Colors 80 cards New: 0Learning: 0Review: 80Relearning: 0Unknown: 0
Colors
80 cards
Review 
Answer
indigo
[anki:play:a:0]
Indigo is a deep and rich color close to the color wheel blue (a primary color in the RGB color space), as well as to some variants of ultramarine, based on the ancient dye of the same name. The word indigo comes from the Latin for "Indian", as the dye was originally imported to Europe from India.
It is traditionally regarded as a color in the visible spectrum, as well as one of the seven colors of the rainbow: the color between blue and violet; however, sources differ as to its actual position in the electromagnetic spectrum.
Review 
Answer
fuchsia
[anki:play:a:0]
Fuchsia is a vivid purplish red color, named after the color of the flower of the fuchsia plant, which was named so by a botanist, Charles Plumier after the 16th century German botanist Leonhart Fuchs.
Review 
Answer
teal
[anki:play:a:0]
Teal is a blue-green colour.
- Its name comes from that of a bird—the common teal (Anas crecca)—which presents a similarly colored stripe on its head.
- The word is often used colloquially to refer to shades of cyan in general.
- Teal is a tertiary color on the RYB color model.
Review 
Answer
magenta
[anki:play:a:0]
Magenta is a colour that is variously defined as purplish-red, reddish-purple or mauvish-crimson. On colour wheels of the RGB (additive) and CMY (subtractive) colour models, it is located exactly midway between red and blue. It is one of the four colours of ink used in colour printing by an inkjet printer, along with yellow, black, and cyan, to make all other colours. The tone of magenta used in printing is called "printer's magenta".
Magenta took its name from an aniline dye made and patented in 1859 by the French chemist François-Emmanuel Verguin, who originally called it fuchsine. It was renamed to celebrate the Italian-French victory at the Battle of Magenta fought between the French and Austrians on June 4, 1859, near the Italian town of Magenta in Lombardy.
Review 
Answer
chartreuse
[anki:play:a:0]
Chartreuse is a color between yellow and green that was named because of its resemblance to the green color of one of the French liqueurs called green chartreuse, introduced in 1764. Similarly, chartreuse yellow is a yellow color mixed with a small amount of green that was named because of its resemblance to the color of one of the French liqueurs called yellow chartreuse, introduced in 1838.
Review 
Answer
violet
[anki:play:a:0]
Violet is the color of light at the short wavelength end of the visible spectrum, between blue and invisible ultraviolet. It is one of the seven colors that Isaac Newton labeled when dividing the spectrum of visible light in 1672. Violet light has a wavelength between approximately 380 and 450 nanometers. The color's name is derived from the violet flower.
Review
Review 
Answer
beige
[anki:play:a:0]
Beige is variously described as a pale sandy fawn color, a grayish tan, a light-grayish yellowish brown, or a pale to grayish yellow.
Review 
Answer
khaki
[anki:play:a:0]
Khaki is a color, a light shade of brown with a yellowish tinge.
- Khaki is an equal mix of sage and buff so it is considered a quinary color.
- Khaki has been used by many armies around the world for uniforms, including camouflage. A khaki uniform is often referred to as khakis.
- In Western fashion, it is a standard color for smart casual dress trousers for civilians, which are also often called khakis.
Review 
Answer
taupe
[anki:play:a:0]
Taupe is a dark gray-brown color. The word derives from the French noun taupe meaning "mole". The name originally referred only to the average color of the French mole, but beginning in the 1940s, its usage expanded to encompass a wider range of shades.
Review 
Answer
crimson
[anki:play:a:0]
Crimson is a strong, red color, inclining to purple. It originally meant the color of the kermes dye produced from a scale insect, Kermes vermilio, but the name is now sometimes also used as a generic term for slightly bluish-red colors that are between red and rose.
Review
Review 
Answer
terracotta
[anki:play:a:0]
Terracotta is a colour that resembles terracotta pottery.
- Terracotta, terra cotta or terra-cotta (Italian: "baked earth", from the Latin terra cocta), a type of earthenware, is a clay-based unglazed or glazed ceramic, where the fired body is porous.
- Terracotta is the term normally used for sculpture made in earthenware, and also for various practical uses including vessels (notably flower pots), water and waste water pipes, roofing tiles, bricks, and surface embellishment in building construction.
- The term is also used to refer to the natural brownish orange color of most terracotta, which varies considerably.
Review
Review 
Answer
periwinkle
[anki:play:a:0]
Periwinkle is a color in the blue and violet family. Its name is derived from the lesser periwinkle or myrtle herb (Vinca minor) which bears flowers of the same color.
Review 
Answer
royal blue (web)
[anki:play:a:0]
Royal blue is both a bright shade and a dark shade of azure blue. It is said to have been created by clothiers in Rode, Somerset, a consortium of whom won a competition to make a dress for Queen Charlotte, consort of King George III.
Review 
Answer
auburn
[anki:play:a:0]
`
Auburn hair is a variety of red hair, most commonly described as reddish-brown in color or dark ginger. Auburn hair ranges in shades from medium to dark. It can be found with a wide array of skin tones and eye colors. The chemical pigments that cause the coloration of auburn hair are frequently pheomelanin with high levels of eumelanin; however, the auburn hair is due to a mutated melanocortin 1 receptor gene in Northwestern European people and by a mutated TYRP1 gene in the Melanesians and Austronesians, both genes that reduce the melanin production of the hair cells.
` Review 
Answer
turquoise
[anki:play:a:0]
Turquoise is a blue/green color, based on the gem of the same name. The word turquoise comes from the French for "Turkish", as the gem was originally imported from Turkey.
Review
Review 
Answer
vermilion
[anki:play:a:0]
Vermilion is both a brilliant red or scarlet pigment, originally made from the powdered mineral cinnabar, and the corresponding color. It was widely used in the art and decoration of Ancient Rome, in the illuminated manuscripts of the Middle Ages, in the paintings of the Renaissance, as sindoor in India, and in the art and lacquerware of China.
Review
Review 
Answer
scarlet
[anki:play:a:0]
Scarlet is a brilliant red color, sometimes with a slightly orange tinge. In the spectrum of visible light, and on the traditional color wheel, it is one-quarter of the way between red and orange, slightly less orange than vermilion. Review 
Answer
burgundy
[anki:play:a:0]
Burgundy is a dark red color.
- It takes its name from the color of Burgundy wine (from the Burgundy region of France, named after the ancient Germanic Burgundians).
- The French call this shade of red after a different wine region, Bordeaux.
Review 
Answer
lilac
[anki:play:a:0]
Lilac is a color that is a pale violet tone representing the average color of most lilac flowers. It can also be described as dark mauve or light blue. The colors of some lilac flowers may be equivalent to the colors shown below as pale lilac, rich lilac, or deep lilac. However, there are other lilac flowers that are colored red-violet.
Review 
Answer
ochre
[anki:play:a:0]
Ochre (from Ancient Greek: ὤχρα, from ὠχρός, ōkhrós, pale) is a natural clay earth pigment which is a mixture of ferric oxide and varying amounts of clay and sand.
- It ranges in colour from yellow to deep orange or brown. It is also the name of the colours produced by this pigment, especially a light brownish-yellow.
- A variant of ochre containing a large amount of hematite, or dehydrated iron oxide, has a reddish tint known as "red ochre" (or, in some dialects, ruddle).
Review 
Answer
navy blue
[anki:play:a:0]
Navy blue got its name from the dark blue (contrasted with naval white) worn by officers in the Royal Navy since 1748 and subsequently adopted by other navies around the world. When this color name, taken from the usual color of the uniforms of sailors, originally came into use in the early 19th century, it was initially called marine blue, but the name of the color soon changed to navy blue.
Review 
Answer
coral
[anki:play:a:0]
The various tones of the color coral are representations of the colors of those cnidarians known as precious corals. Review 
Answer
cobalt blue
[anki:play:a:0]
Cobalt blue is a blue pigment made by sintering cobalt(II) oxide with aluminum(III) oxide (alumina) at 1200 °C. Chemically, cobalt blue pigment is cobalt(II) oxide-aluminium oxide, or cobalt(II) aluminate, CoAl2O4. Cobalt blue is lighter and less intense than the (iron-cyanide based) pigment Prussian blue. It is extremely stable and historically, has been used as a coloring agent in ceramics (especially Chinese porcelain), jewelry, and paint. Transparent glasses are tinted with the silica-based cobalt pigment smalt.
Review 
Answer
lavender
[anki:play:a:0]
Lavender is a shade of purple. It applies particularly to the color of the flower of the same name. The color lavender might be described as a medium purple or a light pinkish purple. The term lavender may be used in general to apply to a wide range of pale, light or greyish purples but only on the blue side. Lilac is pale purple on the pink side. In paints, the colour lavender is made by mixing purple and white paint.
Review 
Answer
amber
[anki:play:a:0]
The color amber is a pure chroma color, located on the color wheel midway between the colors of yellow and orange. The color name is derived from the material also known as amber, which is commonly found in a range of yellow-orange-brown-red colors; likewise, as a color amber can refer to a range of yellow-orange colors.
Review 
Answer
Review 
Answer
tiffany blue
[anki:play:a:0]
Tiffany Blue is the colloquial name for the light medium robin egg blue color associated with Tiffany & Co., the New York City jewelry company created by Charles Tiffany and John Young in 1837. The color was used on the cover of Tiffany's Blue Book, first published in 1845. Since then, Tiffany & Co. has used the color extensively on promotional materials like boxes and bags.
Review 
Answer
sepia
[anki:play:a:0]
Sepia is a reddish-brown color, named after the rich brown pigment derived from the ink sac of the common cuttlefish Sepia. The word sepia is the Latinized form of the Greek σηπία, sēpía, cuttlefish.
Review 
Answer
tyrian purple
Tyrian purple (Ancient Greek: πορφύρα porphúra; Latin: purpura), also known as Phoenician red, Phoenician purple, royal purple, imperial purple, or imperial dye, is a reddish-purple natural dye; the name Tyrian refers to Tyre, Lebanon. It is a secretion produced by several species of predatory sea snails in the family Muricidae, rock snails originally known by the name 'Murex'. In ancient times, extracting this dye involved tens of thousands of snails and substantial labor, and as a result, the dye was highly valued. The main chemical is '6,6′-dibromoindigo.
Review 
Answer
ultramarine
[anki:play:a:0]
Ultramarine is a deep blue color pigment which was originally made by grinding lapis lazuli into a powder. The name comes from the Latin ultramarinus, literally "beyond the sea", because the pigment was imported into Europe from mines in Afghanistan by Italian traders during the 14th and 15th centuries.
Ultramarine was the finest and most expensive blue used by Renaissance painters. It was often used for the robes of the Virgin Mary, and symbolized holiness and humility. It remained an extremely expensive pigment until a synthetic ultramarine was invented in 1826.
Review 
Answer
rose
[anki:play:a:0]
Rose is the color halfway between red and magenta on the HSV color wheel, also known as the RGB color wheel, on which it is at hue angle of 330 degrees. The etymology of the color name rose is the same as that of the name of the rose flower.
Review 
Answer
sienna
[anki:play:a:0]
Sienna (from Italian: terra di Siena, meaning "Siena earth") is an earth pigment containing iron oxide and manganese oxide. In its natural state, it is yellowish brown and is called raw sienna. When heated, it becomes a reddish brown and is called burnt sienna. It takes its name from the city-state of Siena, where it was produced during the Renaissance. Along with ochre and umber, it was one of the first pigments to be used by humans, and is found in many cave paintings. Since the Renaissance, it has been one of the brown pigments most widely used by artists.
Review
Review 
Answer
sky blue
[anki:play:a:0]
Sky blue is a colour that resembles the colour of the unclouded sky at noon (azure) reflecting off a metallic surface.
Review 
Answer
ecru
[anki:play:a:0]
Ecru is the colour of unbleached linen.
- Traditionally ecru was considered a shade of beige, but beginning in the 19th century it became more precisely defined as "a grayish yellow that is greener and paler than chamois or old ivory".
- Ecru comes from the French word écru, which means "unbleached".
Review
Review
Review 
Answer
peach
[anki:play:a:0]
Peach is a color that is named for the pale color of the interior flesh of the peach fruit. This name may also be substituted for "peachy." Like the color apricot, the color peach is paler than most actual peach fruits and seems to have been formulated (like the color apricot) primarily to create a pastel palette of colors for interior design. Review 
Answer
lime
[anki:play:a:0]
Lime is a color that is a shade of yellow-green, so named because it is a representation of the color of the citrus fruit called limes. It is the color that is in between the web color chartreuse and yellow on the color wheel. Alternate names for this color included yellow-green, lemon-lime, lime green, or bitter lime.
Review 
Answer
heliotrope
[anki:play:a:0]
Heliotropium is a genus of flowering plants in the borage family, Boraginaceae. There are around 325 species in this almost cosmopolitan genus, which are commonly known as heliotropes. It is highly toxic for dogs and cats.
Review 
Answer
Review 
Answer
umber
[anki:play:a:0]
Umber is a natural brown or reddish-brown earth pigment that contains iron oxide and manganese oxide. Umber is darker than the other similar earth pigments, ochre and sienna.
In its natural form, it is called raw umber. When heated (calcinated), the color becomes more intense, and then becomes known as burnt umber.
Review
Review
Review 
Answer
cornflower blue
[anki:play:a:0]
Cornflower blue is a shade of medium-to-light blue containing relatively little green compared to blue. This hue was one of the favorites of the Dutch painter Johannes Vermeer.
The most valuable blue sapphires are called cornflower blue, having a medium-dark violet-blue tone.
Review 
Answer
cosmic latte
[anki:play:a:0]
Cosmic latte is the average colour of the universe, found by a team of astronomers from Johns Hopkins University. In 2001, Karl Glazebrook and Ivan Baldry determined that the average color of the universe was a greenish white, but they soon corrected their analysis in a 2002 paper in which they reported that their survey of the light from over 200,000 galaxies averaged to a slightly beigeish white. The hex triplet value for cosmic latte is #FFF8E7. Review
Review 
Answer
saffron
[anki:play:a:0]
Saffron is a shade of yellow or orange, the colour of the tip of the saffron crocus thread, from which the spice saffron is derived. Rajah is a bright deep tone of saffron.
The word saffron ultimately derives (via Arabic) from the Middle Iranian ja'far-. The name was used for the saffron spice in Middle English from c. 1200. As a colour name, it dates to the late 14th century.
Review 
Answer
sapphire
[anki:play:a:0]
Sapphire is a saturated shade of blue, referring to the gem of the same name. Sapphire gems (α-Al2O3) are most commonly found in a range of blue shades although they can be many different colors. Other names for variations of the color sapphire are blue sapphire or sapphire blue, shown below.
Review 
Answer
citrine
[anki:play:a:0]
Citrine is a colour, the most common reference for which is certain coloured varieties of quartz which are a medium deep shade of golden yellow.
The original reference point for the citrine colour was the citron fruit.
Review
Review
Review 
Answer
aquamarine
[anki:play:a:0]
Aquamarine is a color that is a light tint of spring green, in between cyan and green on the color wheel. It is named after the mineral aquamarine (from Latin: aqua marina, "sea water"), a gemstone mainly found in granite rocks. The first recorded use of aquamarine as a color name in English was in 1598.
Review 
Answer
cream
[anki:play:a:0]
Cream is the colour of the cream produced by cattle grazing on natural pasture with plants rich in yellow carotenoid pigments, some of which are incorporated into the fresh milk (specifically, the butterfat). This gives a yellow tone to otherwise-white milk at higher fat concentrations (so the colour of dairy cream could be considered partway between the colours of natural cow’s milk and butter). Cream is the pastel colour of yellow, much as pink is to red. By mixing yellow and white, cream can be produced.
Review 
Answer
tawny
[anki:play:a:0]
Tawny (also called tenné) is a light brown to brownish-orange color.The word means "tan-colored", from Anglo-Norman tauné .
Review 
Answer
cordovan
[anki:play:a:0]
- Cordovan takes its name from the city of Córdoba, Spain, where the production of cordovan leather was first practiced by the Visigoths in the seventh century.
- The term cordovan has come to describe the color of clothing, leather in particular; in this sense, the use of cordovan overlaps with that of oxblood.
Review 
Answer
buff
[anki:play:a:0]
Buff (latin bubalinus) is the light brownish yellow colour of buff leather, an ochreous-like colour. Buff is a mixture of yellow ocher and white: two parts of white lead and one part of yellow ocher produces a good buff, or white lead may be tinted with French ochre alone.It referred to the colour of undyed buffalo leather, such as soldiers wore as some protection.
Review 
Answer
eggplant
[anki:play:a:0]
Eggplant is a dark purple or brownish-purple color that resembles the color of the outer skin of European eggplants. Another name for the color eggplant is aubergine (the French, German and British English word for eggplant).
The first recorded use of eggplant as a color name in English was in 1915.
Review 
Answer
spring green
[anki:play:a:0]
Spring green is a color included on the color wheel that is precisely halfway between cyan and green.
- Spring green is a pure chroma on the color wheel. In HSV color space, the expression of which is known as the RGB color wheel, spring green has a hue of 150°.
- Spring green is one of the tertiary colors on the RGB color wheel. It is also sometimes referred to as mint green.
- The complementary color of spring green is rose.
Review 
Answer
amaranth
[anki:play:a:0]
Amaranth is a reddish-rose color that is a representation of the color of the flower of the amaranth plant.
- The color shown is the color of the red amaranth flower (the color normally considered amaranth), but there are other varieties of amaranth that have other colors of amaranth flowers.
Review
Review 
Answer
slate gray
Slate gray is a gray color with a slight azure tinge that is a representation of the average color of the material slate.
As a tertiary color, slate is an equal mix of purple and green pigments.
Slaty, referring to this color, is often used to describe birds.
Review 
Answer
mahogany
[anki:play:a:0]
Mahogany is a reddish-brown color.
- It is approximately the color of the wood mahogany. However, the wood itself, like most woods, is not uniformly the same color and is not recognized as a color by most.
Review 
Answer
plum
Plum is a purple color with a brownish-gray tinge, like that shown on the right, or a reddish purple, which is a close representation of the average color of the plum fruit.
As a quaternary color on the RYB color wheel, plum is an equal mix of the tertiary colors russet and slate.
Review
Review 
Answer
paris green
[anki:play:a:0]
Paris green (copper(II) acetate triarsenite or copper(II) acetoarsenite) is an inorganic compound. As a green pigment it is also known as Schweinfurt green, emerald green or Vienna green. It is a highly toxic emerald-green crystalline powder[3] that has been used as a rodenticide and insecticide,[4] and also as a pigment, despite its toxicity. It is also used as a blue colorant for fireworks.[5] The color of Paris green is said to range from a pale blue green when very finely ground, to a deeper green when coarsely ground. Review 
Answer
phthalo blue
[anki:play:a:0]
Phthalocyanine Blue BN, also called by many names (EINECS 205-685-1), is a bright, crystalline, synthetic blue pigment from the group of phthalocyanine dyes. Its brilliant blue is frequently used in paints and dyes. It is highly valued for its superior properties such as light fastness, tinting strength, covering power and resistance to the effects of alkalis and acids. It has the appearance of a blue powder, insoluble in most solvents including water.
Review 
Answer
gamboge
[anki:play:a:0]
Gamboge is a partially transparent deep saffron to mustard yellow pigment. It is used to dye Buddhist monks' robes because it resembles the traditional colour used for the robes of Theravada Buddhist monks. It was this pigment that was used to prove Brownian motion by the physicist Jean Perrin in 1908.
Review 
Answer
rust
[anki:play:a:0]
Rust is an orange-brown color resembling iron oxide. It is a commonly used color in stage lighting and appears roughly the same color as photographic safelights when used over a standard tungsten light source.
Rust is named after the resulting phenomenon of the oxidation of iron. The word 'rust' finds its etymological origins in the Proto-Germanic word rusta, which translates to "redness."
Review 
Answer
forest green
[anki:play:a:0]
Forest green refers to a green color said to resemble the color of the trees and other plants in a forest. Review 
Answer
chocolate
[anki:play:a:0]
The color chocolate is a tone of dark brown that resembles chocolate. At right is displayed the color traditionally called chocolate.
This color is a representation of the color of the most common type of chocolate, milk chocolate.
Review
Review
Review 
Answer
orchid
[anki:play:a:0]
Orchid is a bright rich purple color that is a representation of the color of the flower of some members of the plant family orchidaceae.
Various tones of orchid may range from grayish purple to purplish-pink to strong reddish purple.
The word Orchid derives from the Greek word orchis which means testicle, after the appearance of the roots of plants of the genus Orchis.
Declaration of Independence 36 cards New: 0Learning: 0Review: 36Relearning: 0Unknown: 0
Declaration of Independence
36 cards
Review
...a [...] to the opinions of mankind requires that they should declare the causes which impel them to the separation.
Answer
...a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
Review
...a decent respect to the [...] requires that they should declare the causes which impel them to the separation.
Answer
...a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
Review
...a decent respect to the opinions of mankind requires that they should declare the causes which [...] them to the separation.
Answer
...a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
Review
...accordingly all [...], that mankind are more disposed to suffer, while evils are sufferable...
Answer
...accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable...
Review
...accordingly all experience hath shewn, that mankind are more disposed to [...]...
Answer
...accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable...
Review
...and to institute new Government, laying its foundation on [...] and organizing its powers in such form...
Answer
...and to institute new Government, laying its foundation on such principles and organizing its powers in such form...
Review
...and to institute new Government, laying its foundation on such principles and organizing its powers in [...]...
Answer
...and to institute new Government, laying its foundation on such principles and organizing its powers in such form...
Review
...and to provide [...] for their future security.
Answer
...and to provide new Guards for their future security.
Review
...and to provide new Guards for their [...].
Answer
...and to provide new Guards for their future security.
Review
...it is their [...], it is their duty, to throw off such Government...
Answer
...it is their right, it is their duty, to throw off such Government...
Review
...it is their right, it is their [...], to throw off such Government...
Answer
...it is their right, it is their duty, to throw off such Government...
Review
...it is their right, it is their duty, to [...]...
Answer
...it is their right, it is their duty, to throw off such Government...
Review
...than to right themselves by [...] to which they are accustomed.
Answer
...than to right themselves by abolishing the forms to which they are accustomed.
Review
...than to right themselves by abolishing the forms to which they are [...].
Answer
...than to right themselves by abolishing the forms to which they are accustomed.
Review
...that they are endowed by their [...] with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
Answer
...that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
Review
...that they are endowed by their Creator with certain [...], that among these are Life, Liberty and the pursuit of Happiness.
Answer
...that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
Review
...that they are endowed by their Creator with certain unalienable Rights, that among these are [...].
Answer
...that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
Review
...to assume among the powers of the earth, the [...] to which the Laws of Nature and of Nature's God entitle them...
Answer
...to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them...
Review
...to assume among the powers of the earth, the separate and equal station to which the [...] entitle them...
Answer
...to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them...
Review
[...], indeed, will dictate that Governments long established should not be changed for light and transient causes...
Answer
Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes...
Review
But when a [...], pursuing invariably the same Object evinces a design to reduce them under absolute Despotism...
Answer
But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism...
Review
But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under [...]...
Answer
But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism...
Review
Prudence, indeed, will dictate that Governments [...] should not be changed for light and transient causes...
Answer
Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes...
Review
Prudence, indeed, will dictate that Governments long established should not be changed for [...]...
Answer
Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes...
Review
Such has been the [...] of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government.
Answer
Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government.
Review
Such has been the patient sufferance of these Colonies; and such is now the [...] which constrains them to alter their former Systems of Government.
Answer
Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government.
Review
Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to [...].
Answer
Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government.
Review
That to secure these rights, [...] among Men, deriving their just powers from the consent of the governed...
Answer
That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed...
Review
That to secure these rights, Governments are instituted among Men, deriving their [...] from the consent of the governed...
Answer
That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed...
Review
That to secure these rights, Governments are instituted among Men, deriving their just powers from the [...]...
Answer
That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed...
Review
That whenever any Form of Government becomes [...] of these ends, it is the Right of the People to alter or to abolish it...
Answer
That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it...
Review
That whenever any Form of Government becomes destructive of these ends, it is the [...]...
Answer
That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it...
Review
We hold these truths to be [...], that all men are created equal...
Answer
We hold these truths to be self-evident, that all men are created equal...
Review
We hold these truths to be self-evident, that all men are [...]...
Answer
We hold these truths to be self-evident, that all men are created equal...
Review
When in the [...], it becomes necessary for one people to dissolve the political bands which have connected them with another...
Answer
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another...
Review
When in the Course of human events, it becomes necessary for one people to [...] which have connected them with another...
Answer
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another...
English Vocabulary 244 cards New: 0Learning: 0Review: 244Relearning: 0Unknown: 0
English Vocabulary
244 cards
Review
Abdicate (verb)
Answer
Abdicate (verb)
To renounce or relinquish a throne, right, power, or responsibility.
Review
Ablution (noun)
Answer
Ablution (noun)
The washing of one’s body, or part of it, especially as a religious ritual.
The second word part of ablution comes from the Latin verb luo, meaning “wash.” English words that contain the lu root often have something to do with washing, such as deluge, a torrential downpour.
Review
Abnegate (verb)
Answer
Abnegate (verb)
1. To deny or renounce.
2. To relinquish power.
You’re more likely to hear of a queen abdicating the throne and a project manager abnegating responsibility.
Review
Abrogate (verb)
Answer
Abrogate (verb)
1. To abolish by formal, authoritative action; to annul, repeal.
2. To treat as nonexistent; to do away with, set aside.
Abrogate is commonly used with its second sense, as in such phrases as “abrogating responsibility” or “abrogating one’s duty.”
Review
Absquatulate (verb)
Answer
Absquatulate (verb)
To flee, abscond.
“When we returned to our campsite, we realized that the other hiker had absquatulated with most of our gear.”
Review
Acrophobia (noun)
Answer
Acrophobia (noun)
Abnormal fear of heights.
Acrophobia comes from the Greek akros, meaning “at the end, the top, height, summit, or tip.” Related words include acrobatics and acropolis, a high, fortified area of a city.
Review
Adumbrate (verb)
Answer
Adumbrate (verb)
1. To give a sketchy outline of; to suggest, disclose, or outline partially.
2. To foreshadow vaguely; to intimate.
“When quizzed by the English teacher, the student was able to briefly adumbrate the major themes in the novel."
"The first scene in the play, where she notices the new buds on the trees, adumbrates her spiritual rebirth in the second scene.”
Review
Agent provocateur (noun)
Answer
Agent provocateur (noun)
A secret agent hired to incite suspected persons to illegal action that will make them liable to punishment.
Review
Agoraphobia (noun)
Answer
Agoraphobia (noun)
Abnormal fear of open or public spaces.
In ancient Greek cities, the agora was an open area or central marketplace in a city, where citizens could assemble for various social, commercial, and religious activities.
Review
Alacrity (noun)
Answer
Alacrity (noun)
A quick and cheerful readiness and eagerness to do something.
Synonyms for alacrity include vivacity, animation, sprightliness, ebullience, get-up-and-go, vim and vigor, liveliness, zeal, avidity, and expedition.
Review
Antediluvian (adjective)
Answer
Antediluvian (adjective)
1. Of or relating to the period before the biblical flood.
2. Very old-fashioned, out of date, antiquated, or primitive.
Review
Apocryphal (adjective)
Answer
Apocryphal (adjective)
Of doubtful or dubious authenticity; false.
Use the word apocryphal if you want to emphasize that a story or claim is not only probably false but also difficult to verify or find evidence for.
Examples: But it is also probable that these apocryphal versions are based on a genuine original.
This is the most important of all the apocryphal writings for the history of religious thought.
Originally, the Apocrypha were texts that were not included in the Bible because their authenticity could not be firmly established. Today, urban legends are often described as apocryphal because they are passed on by a “friend of a friend.”
Review
Apostate (noun)
Answer
Apostate (noun)
Someone who abandons his or her religion, political beliefs, principles, or cause.
The word comes from the Greek prefix apo-, meaning “away from,” and the Greek verb stenai, meaning “to stand.” In other words, an apostate “stands away from” his or her beliefs.
Synonyms and related words for apostate include backslider, defector, deserter, renegade, heretic, and turncoat.
apostle: apostle came from the Greek verb stellein, meaning “to send.” Thus, an apostle is a messenger “sent away” to spread the word
Review
Argot (noun)
Answer
Argot (noun)
A specialized language characteristic of a particular group of people.
Review
Asperity (noun)
Answer
Asperity (noun)
Roughness or harshness of surface, sound, climate, condition, manner, or temper.
Review
Avuncular (adjective)
Answer
Avuncular (adjective)
1. Of or having to do with an uncle.
2. Resembling an uncle; friendly; helpful; kind, patient, and indulgent.
Review
Badinage (noun)
Answer
Badinage (noun)
Light, playful banter; raillery.
Badinage comes from the French word badiner, meaning “to jest, joke.” It refers to good-natured teasing between people.
Synonyms for badinage include banter, back-and-forth, give-and-take, raillery, and repartee. A related word is riposte, which means “a quick, witty comeback; a sharp reply in speech or action; a counterstroke.” Riposte comes from fencing, where it refers to a quick thrust following a parry of an opponent’s lunge.
Review
Banal (adjective)
Answer
Banal (adjective)
Lacking freshness and originality; trite; commonplace; so ordinary as to
have become tedious.
Banal is often used alongside such collocates as comments, observations, and remarks.
Synonyms for banal include trite, stale, threadbare, and hackneyed.
Review
Bedlam (noun)
Answer
Bedlam (noun)
A place or situation of noisy uproar and confusion.
Review
Bellicose (adjective)
Answer
Bellicose (adjective)
Warlike, pugnacious, aggressively hostile.
Example: Squirrels are restless, courageous and pugnacious little animals.
Bellicose shares the root bell with a number of other words, such as belligerence, antebellum, and rebellion. This root is from the Latin noun bellum, meaning “war.”
A good key word for the root bell is rebellion.
Belligerent is a close synonym for bellicose that shares the root bell and also means “warlike and aggressively hostile.”
Review
Berth (noun)
Answer
Berth (noun)
a ship's allotted place at a wharf or dock
or
(of a passenger ship) provide a sleeping place for (someone).
a ship's allotted place at a wharf or dock
or
(of a passenger ship) provide a sleeping place for (someone).
Review
Bête noire (noun)
Answer
Bête noire (noun)
A person or thing that is particularly disliked, dreaded, or avoided.
Review
Billingsgate (noun)
Answer
Billingsgate (noun)
Foul, coarse, abusive language.
Review
Blandishment (noun)
Answer
Blandishment (noun)
Flattery that is designed to persuade a listener to do something.
Review
Bloviate (verb)
Answer
Bloviate (verb)
To talk pompously; to talk at great length in a pompous and boastful manner.
Bloviate is an Americanism that sounds like what it means. It is derived from blow, which brings to mind a blowhard who blows hot air.
Review
Bombast (noun)
Answer
Bombast (noun)
Pretentious, pompous, grandiloquent speech or writing.
We often see the adjective form of bombast, bombastic, used alongside the collocates prose, speech, and writing, as in such phrases as a politician’s bombastic speech or the author’s bombastic prose.
Synonyms:
Turgid comes from a Latin word meaning “to swell” and can refer to "swollen", overblown, inflated language or to physically swollen things, such as rivers.
Orotund comes from the Latin phrase ore rotundo, meaning “with rounded mouth,” and somewhat paradoxically, has either a positive or a negative connotation, depending on how it’s used. Orotund can be positive when referring to a resonant, booming voice and negative when referring to bombastic speech or writing.
Use verbose when you want to emphasize that the speech uses more words than needed. Another synonym for overly wordy language is prolix.
Use flowery when you want to describe language that includes overly ornate images and expressions.
Use pretentious when you want to emphasize language that is intentionally inflated to impress.
Review
Bowdlerize (verb)
Answer
Bowdlerize (verb)
To change a text by removing or modifying parts that could offend people.
It came from an English physician named Thomas Bowdler, who, in the early 19th century, decided that Shakespeare’s plays were too risqué to be appropriate for the public.
"every edition of his letters and diaries has been bowdlerized"
"every edition of his letters and diaries has been bowdlerized"
Review
Braggadocio (noun)
Answer
Braggadocio (noun)
1. A braggart.
2. Empty, arrogant boasting.
Yet knight he was not, but a boastfull swaine,
That deedes of armes had ever in despaire,
Proud Braggadocchio, that in vaunting vaine
His glory did repose, and credit did maintaine.
Review
Bravado (noun)
Answer
Bravado (noun)
A pretentious, swaggering display of courage intended to impress others.
Bravado refers to an outward display of bluster and false bravery used to cover up insecurity and fear.
Review
Brobdingnagian (adjective)
Answer
Brobdingnagian (adjective)
Immense, enormous.
Review
Bromide (noun)
Answer
Bromide (noun)
A platitude or trite saying
Bromide originally referred to a sedative, specifically, a chemical compound of bromine and another metal. Of course, sedatives deaden and dull the senses, leading to the more figurative meaning of bromide: trite sayings that have become so overused they deaden our senses.
Review
Bumptious (adjective)
Answer
Bumptious (adjective)
Pushy; offensively or loudly self-assertive; cocky.
Bumptious describes a different type of arrogance than supercilious. With bumptious, the focus isn’t on scornful disdain but on the loud and pushy aspects of arrogance.
"an impossibly bumptious and opinionated ass"
"an impossibly bumptious and opinionated ass"
Review
Bunk (noun)
Answer
Bunk (noun)
Foolish, untrue talk; nonsense.
Review
Cabal (noun)
Answer
Cabal (noun)
1. A small group of people secretly working together.
2. A secret plot.
Cabal originally comes from Kabbala, a Jewish mystical method of interpreting scripture that became associated with the secret and the occult.
Review
Cachet (noun)
Answer
Cachet (noun)
Superior status, privilege.
“On the university campus, wearing North Face jackets and UGG boots carries a certain cachet among college students.”
Review
Caesura (noun)
Answer
Caesura (noun)
A break or pause.
In prosody—the study of poetic meter—and in musical composition, a caesura is a small pause in the middle of a line of verse or music.
Caesura is borrowed directly from the Latin noun caesura, which again, comes from the verb caedo, “to cut.”
Review
Callow (adjective)
Answer
Callow (adjective)
Immature or inexperienced; lacking adult sophistication.
Callow is used to describe people who don’t have much life experience or don’t know how to behave like adults, as in the phrase callow youth.
Synonyms for callow include immature, untried, green, raw, unfledged, and unripened
Callow comes from the Old English word calu, meaning “bare, bald,” which was sometimes applied to young birds with no feathers.
Review
Calumny (noun)
Answer
Calumny (noun)
A false accusation maliciously intended to destroy someone’s reputation.
“Instead of basing his attacks on the president’s actual policies, the candidate resorted to calumny to try to smear the chief executive’s reputation.”
The verb form of calumny is calumniate
Review
Canoodle (verb)
Answer
Canoodle (verb)
1. To kiss and cuddle; pet, caress; fondle.
2. To coax; persuade or cajole; wheedle.
“It seems as if the main purpose of some of today’s reality TV is to show various couples canoodling.”
“His success as a lobbyist could be attributed to his ability to canoodle politicians.”
Review
Capacious (adjective)
Answer
Capacious (adjective)
Capable of containing a great deal; spacious and roomy.
Review
Captious (adjective)
Answer
Captious (adjective)
Fault finding; hypercritical; difficult to please.
Review
Castigate (verb)
Answer
Castigate (verb)
To punish, rebuke, or criticize severely.
When you castigate someone, you are casting punishments and criticisms.
Review
Chutzpah (noun)
Answer
Chutzpah (noun)
Personal confidence or courage; shameless audacity; impudence.
“Even though she shocks and comes across to some folks as rude, I admire her chutzpah; she speaks her mind and gets things done.”
Chutzpah comes from a Yiddish word meaning “impudence, gall.”
“that quality enshrined in a man who, having killed his mother and father, throws himself on the mercy of the court because he is an orphan.”
Synonyms for chutzpah include audacity, nerve, impudence, and insolence; related adjectives include brazen, brash, cheeky, and saucy.
Review
Circumlocution (noun)
Answer
Circumlocution (noun)
Evasive, long-winded rambling or indirect speech.
Review
Circumspect (adjective)
Answer
Circumspect (adjective)
Cautious, prudent.
Circumspect is a combination of circum (“around”) and spect (“look”). To remember this word, think of a cautious person “looking around” before he or she acts.
Review
Claptrap (noun)
Answer
Claptrap (noun)
Pretentious nonsense; insincere speech.
English has at least 40 synonyms for claptrap, including sham, hokum, tripe, tosh, bosh, rubbish, humbug, poppycock, balderdash, blarney, bombast, babble, blather, twaddle, and many others.
Review
Cleave (verb)
Answer
Cleave (verb)
1. To split or divide by cutting.
2. To stick closely to; to cling to.
Review
Commodious (adjective)
Answer
Commodious (adjective)
Comfortably or conveniently spacious; roomy.
Review
Concatenation (noun)
Answer
Concatenation (noun)
A series of things that are linked together.
Review
Contumacious (adj.)
Answer
Contumacious (adj.)
Stubbornly disobedient and rebellious to authority; willfully obstinate.
Review
Coterie (noun)
Answer
Coterie (noun)
A small, often select group of people who associate with one another frequently and share a common interest, background, or purpose.
Coterie has a similar meaning to cabal but without the added sense of secrecy and the connotation of treachery. For example: “A tightknit coterie of presidential advisors made all the important decisions in the administration.”
Synonyms and related words for coterie include sisterhood or brotherhood, society, troop, sect (often used to identify a religious group that may be exclusive and may deviate from mainstream religious traditions), faction (often a dissentious unit within a larger group), clique (a snobby, exclusive group), band, ring, circle, cadre, gang, and clan.
"a coterie of friends and advisers"
"a coterie of friends and advisers"
Review
Craven (adjective)
Answer
Craven (adjective)
Very cowardly; abjectly afraid.
Someone described as craven is spineless or chickenhearted. Craven politicians, for instance, are afraid to stand up for what they believe and deserve no respect; indeed, their lack of heart inspires contempt. Use craven to describe cowardly people, actions, speeches, and decisions.
Review
Deduction (noun)
Answer
Deduction (noun)
The process of reasoning in which a conclusion necessarily follows from the stated premises.
Review
Denude (verb)
Answer
Denude (verb)
To lay bare; to strip; to make nude.
“The constant criticism by the captious boss denuded the small company of its once tightknit camaraderie.”
Review
Déshabille (noun)
Answer
Déshabille (noun)
A state of being dressed in a very casual or even careless, disheveled, and disorderly style.
Review
Desuetude (noun)
Answer
Desuetude (noun)
A state of disuse or inactivity.
You’ll often see desuetude used with its collocate, fall, to indicate that something gradually deteriorated into a state of disuse, as in: “fallen into desuetude.”
Desuetude comes from the Latin prefix de-, meaning “away from,” and the Latin verb suesco, meaning “to become accustomed.” If you neglect things for too long, you become unaccustomed to them, and eventually, they’re no longer useable. They fall into desuetude
through neglect.
Review
Detritus (noun)
Answer
Detritus (noun)
Disintegrated or eroded matter; debris.
“The detritus of battle littered the city, with crumbled buildings and smoking hulks of vehicles everywhere.”
Both detriment and detritus ultimately come from the Latin verb detero, meaning “to wear away.” Something that is detrimental to your health, such as drinking too much, “wears away” at your health, and detritus is debris that’s been “worn away.”
Review
Dialect (noun)
Answer
Dialect (noun)
A variety of a language often associated with a certain region or social class.
Review
Diaspora (noun)
Answer
Diaspora (noun)
The movement, migration, or scattering of a people away from an established or ancestral homeland.
Diaspora comes from two Greek words, dia and speirein, that were joined together as a compound word meaning “to scatter across.”
Review
Didactic (adjective)
Answer
Didactic (adjective)
Inclined to teach or moralize excessively.
Didactic carries with it a connotation of preachy and boring. For example: “The professor’s didactic lecture style was known for putting her students to sleep.”
Synonyms for didactic include preachy, donnish, and sermonize.
Pedantic is another synonym, but it has a slightly different meaning: characterized by a narrow, often ostentatious concern for book learning and formal rules. In other words, didactic emphasizes excessive teaching, while pedantic emphasizes excessive attention to trivia, often to show off.
Review
Dilettante (noun)
Answer
Dilettante (noun)
A dabbler in the arts or some field of knowledge; often used in a pejorative sense.
Synonyms and related words for dilettante include amateur, dabbler, layperson, do-it-yourselfer, nonprofessional, rookie, and if you want to emphasize the “imposter” aspect of a dilettante, poser and pretender.
Review
Diminuendo (noun)
Answer
Diminuendo (noun)
A decrease in loudness or intensity.
Review
Discursive (adjective)
Answer
Discursive (adjective)
Rambling from topic to topic, aimless, digressive.
The word discursive comes from the Latin verb discurro, which means “to run to and fro” or “to wander.”
Review
Dissemble (verb)
Answer
Dissemble (verb)
To disguise or conceal behind a false appearance.
Dissemble is related to the English word resemble and comes from the Latin simulo, meaning “pretend, assume, simulate.”
Review
Dogmatic (adjective)
Answer
Dogmatic (adjective)
Characterized by an authoritative, arrogant assertion of unproven ideas.
Review
Donnybrook
Answer
Donnybrook
A free-for-all; a brawl; a scene of disorder and uproar.
Donnybrook is a suburb of Dublin that was known for an annual fair that incited a number of no-holds-barred, drunken, riotous brawls. The situation became so bad that the fair was banned in 1855.
Synonyms:
* Melee: a confused, rowdy fight.
* Fracas: a noisy disturbance, a quarrel, an uproar, perhaps even a physical confrontation.
* Row: an upheaval, a freefor-all, a rumble.
Milder synonyms: loggerheads, scrap, scuffle, flap, tussle, spat, dustup.
Confused situations: kerfuffle, imbroglio
Review
Draconian (adjective)
Answer
Draconian (adjective)
Exceedingly harsh; very severe; cruel.
Review
Éminence grise (noun)
Answer
Éminence grise (noun)
1. A powerful decision maker or advisor who operates behind the scenes.
2. An elder statesman or eminent senior member of a group.
Review
Eponym (noun)
Answer
Eponym (noun)
A word derived from a person’s name.
Review
Equivocal (adjective)
Answer
Equivocal (adjective)
Open to two or more interpretations, often with an intent to mislead or to be purposely vague.
Review
Ersatz (adj.)
Answer
Ersatz (adj.)
Describes an inferior substitute
During World War II, British POWs were served ersatzbrot, or “substitute bread,” made from low-quality potato starch, flour, and even sawdust.
Review
Erudite (adjective)
Answer
Erudite (adjective)
Learned or scholarly; characterized by deep and extensive knowledge.
Derived from the Latin preposition ex (“out of”) and the Latin adjective rudis (“unpolished,
rough, unlearned”). Those who are erudite are literally “brought out of a rough, raw, unlearned state”—polished through education.
Synonyms for erudite include lettered, brainy, scholarly, and learned.
Review
Esoteric (adjective)
Answer
Esoteric (adjective)
Understood by only a select group.
Review
Evanescent (adjective)
Answer
Evanescent (adjective)
1. Fleeting, of short duration, vanishing or likely to vanish.
2. Fragile, diaphanous, and unsubstantial.
Review
Execrate (verb)
Answer
Execrate (verb)
1. To damn or denounce scathingly; curse.
2. To detest utterly, abhor, abominate, loathe.
Use execrate when you want to stress a denunciation filled with intense loathing, hatred, and passionate fury.
Curse and damn both suggest angry denunciation by blasphemous oaths. Curse sometimes comes across as a bit more literary than damn.
Use anathematize to describe a more formal, solemn, impassioned denunciation or condemnation, such as a denunciation by a priest from the pulpit. Anathematize is the verb form of the noun anathema, meaning, “something that is hated.”
Execrate comes from the Latin prefix ex-, meaning “out of, from, away,” and the Latin word sacro, meaning “to devote to, to mark as sacred.” Thus, execrate is literally “to take the sacred away,” or to curse.
Review
Exegesis (noun)
Answer
Exegesis (noun)
An explanation or critical interpretation, especially of the Bible or another religious text.
Review
Exiguous (adjective)
Answer
Exiguous (adjective)
Excessively scanty, inadequate, and meager.
Synonyms for exiguous include inadequate, hand-tomouth, scant, scarce, skimpy, spare, and sparse.
We often see exiguous used with one of several collocates: resources, supplies, finances, or evidence.
Review
Extirpate (verb)
Answer
Extirpate (verb)
To pull up by the roots; to root out and destroy completely; to wipe out.
ex-, meaning “out,”
stirps, meaning “a root, stock of a tree.”
Review
Facile (adjective)
Answer
Facile (adjective)
Done or achieved with little effort or difficulty; easy; performed with effortless ease and fluency.
“A facile person has the facility to facilitate work.”
Review
Factitious (adj.)
Answer
Factitious (adj.)
1. Made or manufactured; not natural.
2. Made up in the sense of contrived; a sham, fake, or phony.
(1) “The CIA agent hid his message inside the hollow factitious rock by the bridge; his handler would pick up the message a few hours later”
(2) “My dad's factitious smile didn't fool anyone; he was definitely not happy to see our cousins show up once again unannounced.”
Review
Factotum (noun)
Answer
Factotum (noun)
Someone hired to do a variety of jobs; a jack-of-all-trades.
Tessa, the office factotum, does the bulling, answers the phones, helps out in the PR department, and even knows how to cook a mean blueberry scone—she’s indispensable!
From latin fac, to make or do, and totum, all.
Review
Feckless (adjective)
Answer
Feckless (adjective)
1. Weak and ineffective.
2. Worthless, lazy, and irresponsible.
Review
Fin de siècle (noun phrase)
Answer
Fin de siècle (noun phrase)
End of the century.
The phrase fin de siècle can be applied to the end of any century, but it is more commonly used to describe the end of the 19th century, particularly its culture of sophisticated despair and ennui. Here’s an example in which the word applies to that period: “Fin de siècle Vienna became a major hub for artists of the Secession movement.”
Review
Foment (verb)
Answer
Foment (verb)
To stir up, incite, rouse, provoke, inflame, encourage, or instigate.
Foment is often used alongside its collocates riot, insurrection, and rebellion, as in, “A few hardcore guerillas attempted to foment a widespread insurrection against the brutal dictatorship.”
Review
Fortitude (noun)
Answer
Fortitude (noun)
Mental and emotional strength in facing difficulty, adversity, danger, or temptation courageously.
Review
Fractious (adjective)
Answer
Fractious (adjective)
Unruly; hard to manage; rebellious.
Fractious is close in meaning to one of our target words from an earlier lecture, contumacious, an adjective meaning stubbornly rebellious; willfully and obstinately disobedient.
The root fract in fractious is derived from the verb Latin frango, meaning “to break.”
Review
Frisson (noun)
Answer
Frisson (noun)
An almost pleasurable sensation of fright.
Frisson came into English in the 1700s from the French word frisson, meaning “shiver, thrill,” which came from the Latin frigeo, “to be cold.”
Review
Fulminate (verb)
Answer
Fulminate (verb)
1. To issue a thunderous verbal attack; to vehemently denounce.
2. To explode with sudden violence; to detonate.
Fulminate comes from the Latin word fulmen, meaning “a lightning flash"
Synonyms for fulminate include rail against, upbraid, denounce, lambaste, berate, castigate, and excoriate.
Review
Fulsome (adj)
Answer
Fulsome (adj)
1. Excessively or insincerely lavish.
2. Abundant.
Review
Gadfly
Answer
Gadfly
1. A persistently annoying person who questions, critiques, and pesters.
2. An insect that annoys livestock by biting and sucking their blood.
Informal synonyms for gadfly include nag, pest, and thorn in the side. Another wonderful synonym for gadfly is a word
borrowed from Yiddish, nudnik, meaning “a dull, boring pest.”
Review
Gerrymander (noun/verb)
Answer
Gerrymander (noun/verb)
noun: The act of dividing election districts to give one party an unfair advantage.
verb: To divide election districts unfairly.
Review
Gestalt (noun)
Answer
Gestalt (noun)
A pattern possessing qualities as a whole that cannot be described merely as a sum of its parts.
Review
Glossophobia (noun)
Answer
Glossophobia (noun)
Unreasonable fear of speaking in public.
Gloss or glot are two roots derived from the Greek word glossa, meaning “tongue.” This root is also seen in polyglot, a person who can speak many languages, as well as glottis, epiglottis, and glottal.
Review
Gordian knot (noun phrase)
Answer
Gordian knot (noun phrase)
An exceedingly complicated and intricate problem or deadlock; an intractable problem.
Review
Halcyon (adjective)
Answer
Halcyon (adjective)
Tranquil, calm, and peaceful; may refer to happy, joyful, and prosperous times.
Collocates: halcyon days, halcyon times.
In Greek mythology, Alcyone was the daughter of Aeolus, the god of the winds. She was turned into a bird, the halcyon or kingfisher, which some believed brooded its eggs on a floating nest.
Review
Harrumph (verb)
Answer
Harrumph (verb)
1. To make a pretentious show of clearing one’s throat.
2. To offer brief critical comments.
Tintinnabulation, susurration, and harrumph are all onomatopoeic; that is, they sound like the sounds they refer to: ringing bells, whispering, and ostentatious throat-clearing.
Review
Hobson’s choice (noun phrase)
Answer
Hobson’s choice (noun phrase)
A choice between what is available and nothing; the absence of a real alternative.
Review
Hoi Polloi (noun)
Answer
Hoi Polloi (noun)
The ordinary masses; the common people.
Hoi polloi is a transliteration of two Greek words that literally mean “the many.”
Review
Homograph (noun)
Answer
Homograph (noun)
One of two or more words that are spelled the same but have different pronunciations and meanings.
Review
Homonym (noun)
Answer
Homonym (noun)
One of two or more words that are spelled and pronounced the same but carry different meanings.
Review
Hornswoggle (v.)
Answer
Hornswoggle (v.)
To swindle, cheat, or dupe.
Two fun synonyms for hornswoggle are bamboozle and hoodwink.
Review
Hubris (noun)
Answer
Hubris (noun)
Excessive pride or self-confidence; arrogance.
Review
Imbroglio (noun)
Answer
Imbroglio (noun)
1. A state of great confusion and entanglement; a complicated, difficult, or embarrassing situation.
2. A complex misunderstanding, disagreement, or dispute—sometimes of a bitter nature.
Example: The curious imbroglio deceived royalists and republicans alike.
He skilfully avoided entanglement in the Jackson-Calhoun imbroglio.
Imbroglio comes from an Italian word that means “to confuse” and is related to the English word embroiled, which means “thrown into a state of confusion.” Also related to broil, broth, and brew.
Kerfuffle is a synonym for imbroglio of Scot-Gaelic origin; it also refers to a commotion, controversy, or fuss. Other synonyms include brouhaha, hullabaloo, hubbub, and hurly-burly
Review
Impetuous (adjective)
Answer
Impetuous (adjective)
Acting or done quickly and without thought or care. Impulsive, reckless, hasty.
Acting or done quickly and without thought or care. Impulsive, reckless, hasty.
Review
Importune (verb)
Answer
Importune (verb)
To harass with repeated requests; to demand of someone insistently.
Review
Inchoate (adjective)
Answer
Inchoate (adjective)
1. Not completely formed or developed; only partly in existence.
2. Not organized; lacking order.
Both nascent and inchoate refer to the beginning stages of something, but inchoate, depending on how it’s used, sometimes emphasizes what is not present in the beginning stages, focusing on the more “lacking” aspects of a beginning. This is in contrast to nascent, which could stress the more developing, growing, positive aspects of the beginning stages.
“Her nascent idea for a new software application wasn’t completely thought out yet, but it had such potential that investors were already lining up.”
“Her inchoate idea for a new software application wasn’t completely thought out yet, which meant that she had a lot of work to do before investors lined up.”
Review
Indolent (adjective)
Answer
Indolent (adjective)
Habitually lazy and slow; tending to avoid exertion.
Indolent is used to describe laggards, slackers, loafers, clockwatchers, do-nothings, malingerers, and procrastinators.
Synonyms for indolent include sluggish, idle, lackadaisical, languid, lethargic, listless, and slothful.
Review
Induction (noun)
Answer
Induction (noun)
The process of inferring general principles from individual facts or instances.
Review
Ingénue (noun)
Answer
Ingénue (noun)
1. An innocent, naïve girl or young woman.
2. A stock innocent character in a movie or play or the actress playing
such a character.
Review
Insidious (adjective)
Answer
Insidious (adjective)
Intended to entrap, ensnare, or beguile; stealthily treacherous or deceitful.
This word is derived from the Latin insidere, meaning “to sit in or on.” Thus, insidious is used to describe a type of evil that works on the inside—an inside job that is secret, stealthy, and harmful.
Review
Insipid (adjective)
Answer
Insipid (adjective)
Bland and lacking in flavor; lacking in interesting, exciting, or stimulating qualities.
Insipid is often used to describe food, as in the following sentence: “The novice chef left the roast in the oven too long, cooking out all the spices and rendering the meat insipid.” But the word can also apply to anything that lacks interest or excitement; for example: “The insipid, overly defensive style of both soccer teams resulted in a nil-nil draw and the most boring match the fans had seen in years.”
Synonyms for insipid include tasteless, bland, and flat.
Review
Insouciant (adjective)
Answer
Insouciant (adjective)
Free from concern, worry, or anxiety; carefree; nonchalant.
Review
Intrepid (adjective)
Answer
Intrepid (adjective)
Resolutely fearless, dauntless.
Intrepid comes from the Latin in, meaning “not,” and trepidus, an adjective that means “alarmed, scared.” Trepidus is related to the Latin verb trepido, meaning “tremble.” Thus, to be intrepid is to not be alarmed or scared, to not tremble, even in the face of danger.
Review
Inure (verb)
Answer
Inure (verb)
To become accustomed to something undesirable, such as hardship, difficulty, or pain; to toughen or harden; to habituate.
“Living in the wild for 30 years, the stoic hermit had become inured to cold and want.”
Review
Invidious (adjective)
Answer
Invidious (adjective)
Creating ill will, envy; causing resentment; unfairly or offensively discriminating.
This word comes from the Latin invidia, meaning “envy.”
Review
Jargon (noun)
Answer
Jargon (noun)
Unintelligible or meaningless speech.
Review
Jeremiad (noun)
Answer
Jeremiad (noun)
A long lamentation or complaint; a bitter lament; a scolding speech or sermon.
Jeremiad is named after the Old Testament prophet Jeremiah, who prophesied the imminent
downfall of the Kingdom of Judah.
Often, jeremiad refers to a bitter lament about the state of society, particularly one containing a prophecy of doom. For example: “Her article was yet another jeremiad describing and lamenting the decay of morals in today’s society.”
Review
Juggernaut (noun)
Answer
Juggernaut (noun)
An overwhelming or unstoppable force that smashes everything in its path.
Review
Laconic (adjective)
Answer
Laconic (adjective)
Using few words, terse, brief, succinct, taciturn, concise.
Review
Lacuna (noun)
Answer
Lacuna (noun)
A gap or hole where something should be.
Lacuna is often used to refer to a missing section of a book that has been censored or to a part of an ancient text that has gone missing. For example: “Although the ancient manuscript was recovered, the notably large lacuna at the beginning made the text confusing.”
In medicine, lacuna can refer to a small cavity in an anatomical structure, such as a bone.
Lacuna comes from the Latin lacuna, meaning “hole or pit.” Related words include lake and lagoon
Review
Lagniappe (noun)
Answer
Lagniappe (noun)
A small gift given by a storeowner to a customer; any small extra gift or benefit.
Review
Lilliputian (adjective)
Answer
Lilliputian (adjective)
1. Very small, diminutive.
2. Trivial, petty.
Review
Lingua franca (noun)
Answer
Lingua franca (noun)
A common language used by speakers of different languages to communicate.
Review
Luddite (noun)
Answer
Luddite (noun)
Anyone who opposes the introduction of technological change.
Review
Machinations (noun)
Answer
Machinations (noun)
Intrigues, plots, crafty schemes, or the act of plotting.
In fact, the word political is by far the most common collocate
with machinations, as in political machinations. Devious,
corrupt, and evil are other adjectives commonly found before the
word machinations.
Review
Magnum opus (noun)
Answer
Magnum opus (noun)
An artist’s greatest work.
Review
Maladroit (adjective)
Answer
Maladroit (adjective)
Awkward, clumsy, tactless, or bungling.
Review
Malaise (noun)
Answer
Malaise (noun)
A vague or indefinite feeling of unease or discomfort.
As in economic malaise
Review
Malapropism (noun)
Answer
Malapropism (noun)
A ridiculous and often humorous misuse of words, particularly words that sound similar but are different in meaning.
Review
Malcontent (noun)
Answer
Malcontent (noun)
A person who is chronically dissatisfied.
A great synonym for a complainer or whiner is a kvetcher. Kvetch is an Americanism from Yiddish that literally means “to squeeze, pinch, or press.”
Review
Malediction (noun)
Answer
Malediction (noun)
A curse; evil talk about someone; slander.
Review
Malefactor (n.)
Answer
Malefactor (n.)
A criminal; a person who violates the law.
Review
Malfeasance (n.)
Answer
Malfeasance (n.)
An illegal or harmful act, usually committed by a public official, that violates the public trust.
Review
Malinger (verb)
Answer
Malinger (verb)
To fake or exaggerate illness, usually to avoid work.
Review
Manumit (verb)
Answer
Manumit (verb)
To release from slavery or servitude.
Manumit comes from two Latin roots: man (“hand”) and mit, from the Latin verb mitto, meaning “send, let go, release.”
Review
Maudlin (adj.)
Answer
Maudlin (adj.)
Foolishly, tearfully, and weakly sentimental; overly emotional.
Maudlin is derived from an alteration of the name Mary
Magdalene, one of the most prominent women described in the
New Testament. In the Middle Ages, Mary Magdalene was often depicted in paintings as a weeping, repentant sinner. This tearful image led to the current figurative meaning of maudlin—overly sentimental.
Synonyms and related words for maudlin and sentimental include schmaltzy, gushing, drippy, and hokey.
Review
Maunder (verb)
Answer
Maunder (verb)
To talk aimlessly and incoherently.
Synonyms for maunder include babble and prattle, which means “to chatter meaninglessly and at length.”
Most sources state that maunder is probably related to, or a dialectical variant of, meander, which means “to wander aimlessly” and originally referred to winding rivers.
Review
Maw (noun)
Answer
Maw (noun)
The mouth, throat, or gullet of an animal, particularly a carnivorous animal.
English has a large number of synonyms and related words for maw or mouth, including craw, gullet, jaws, muzzle, piehole, gob, yap, trap, chops, and kisser.
Review
Mawkish (adj.)
Answer
Mawkish (adj.)
Excessively and objectionably sentimental.
Mawkish is another synonym for maudlin, but there is an important distinction in meaning between these two words. As described in Merriam-Webster’s Dictionary of Synonyms, mawkish is an adjective that emphasizes the sickening nature of the sentiment. In other words, mawkish sentiment is often disgusting and sickening because it’s so incredibly insincere or over the top.
Mawkish comes from the Middle English word
mawke, which means “maggot.”
Review
Mercurial (adjective)
Answer
Mercurial (adjective)
1. Liable to sudden and unpredictable change; volatile; erratic.
2. Animated, lively, quick-witted.
Review
Misanthrope (noun)
Answer
Misanthrope (noun)
Someone who hates and distrusts all people
Review
Mollycoddle (v.)
Answer
Mollycoddle (v.)
To overindulge; to treat with excessive attention to the point of spoiling someone.
Coddle means to indulge and treat tenderly. Molly was originally a term of contempt for a man who pampered himself too much.
Review
Mordant (adjective)
Answer
Mordant (adjective)
Bitingly sarcastic.
Someone who is mordant has the ability to drive home disagreeable truths in a
sardonic, caustic manner. Mordant comments imply insensitiveness or even outright maliciousness in intent. Thus, mordant is a bit nastier than trenchant.
Caustic is a close synonym for mordant.
Use acrid when you want to stress bitterness or even malevolence.
Scathing criticism, although fierce, can come from a good motive. In contrast, mordant criticism often implies ill intent.
From Latin mordeo, meaning “to bite, bite into; nip; sting.” Mordant is also related to the English word morsel, meaning “a small bite of something.”
Review
Moribund (adjective)
Answer
Moribund (adjective)
1. Approaching death; coming to an end.
2. No longer effective or active; stagnant; not progressing or advancing.
Moribund comes from the Latin word morior, which means “to die.” This same Latin verb also gives us the fertile root mort. The following words are derived from this powerful root: mortal, immortal, mortality, mortuary, postmortem, mortify, and rigor mortis.
Review
Mot juste (noun)
Answer
Mot juste (noun)
The exact, appropriate word or expression for a situation.
Review
Mountebank (noun)
Answer
Mountebank (noun)
A flamboyant swindler; a flimflammer; someone who claims to be an expert but isn't.
Mountebank comes from an Italian phrase meaning to “mount a bench” and refers to a quack doctor or swindler, who would enter a town, mount a bench in the public square to draw a crowd, and try to sell fake potions to a susceptible public.
Review
Moxie (noun)
Answer
Moxie (noun)
1. The ability to face difficulty with spirit and courage.
2. Aggressive energy, vigor, verge, and pep or skill and know-how.
Review
Mugwump (noun)
Answer
Mugwump (noun)
1. A person, especially a politician, who is unable to make up his or her mind on an issue.
2. A person who remains neutral or independent on a controversial issue.
Review
Nascent (adjective)
Answer
Nascent (adjective)
Emerging, developing, coming into existence, forming.
Nascent can be used to describe the birth of anything, including an idea, a newly formed group, or a movement. For example: “Her nascent idea for a new software application wasn’t completely thought out yet, but it had such incredible potential that investors were already lining up.”
Synonyms for nascent include incipient, burgeoning, embryonic, fledgling, and evolving.
Nascent comes from the Latin root nasc, which in turn comes from the Latin word nascor, meaning “to be born.” Another root from this Latin verb is nat. Related words that share this root and have something to do with birth include nativity, natal, prenatal, innate, native, and neonatal.
Review
Nihilism (noun)
Answer
Nihilism (noun)
A belief in nothing.
Review
Noisome (adjective)
Answer
Noisome (adjective)
Offensive to the point of arousing disgust; foul, particularly in reference
to an odor.
Noisome describes odors that are disgusting and distasteful; it also carries a second meaning of noxious, harmful, or unwholesome. Synonyms and related words for noisome include loathsome, offensive, disgusting, and to emphasize the decaying and rotting aspects of disgusting smells, fetid and putrid.
Review
Nonpareil (adjective)
Answer
Nonpareil (adjective)
Without peer; having no equal.
Nonpareil comes from the 15th-century French words non (meaning “not”) and pareil (meaning “equal”). Combining these two yields “not equal,” meaning someone or something that is without equal.
Synonyms for nonpareil include matchless, peerless, inimitable, unrivaled, unsurpassed, and incomparable.
Review
Obloquy (noun)
Answer
Obloquy (noun)
1. Harshly critical speech or verbal abuse.
2. The disgrace that results from such abuse.
ob- “against, in opposition to.” Thus, obloquy is “speech made against others.”
"he endured years of contempt and obloquy"
"he endured years of contempt and obloquy"
Review
Obsequious (adjective)
Answer
Obsequious (adjective)
Servile and fawning; overly deferential.
Obsequious contains the Latin root usually spelled sequ or sec and meaning “follow”; in other words, obsequious people follow others to gain their favor. This fertile root also gives us sequence, non sequitur, sequel, consecutive, persecute, second, sect, consequence, and subsequent.
Review
Oenophile (noun)
Answer
Oenophile (noun)
A connoisseur or lover of wine.
Review
Officious (adjective)
Answer
Officious (adjective)
Marked by excessive, often aggressive eagerness in offering unwanted advice, service, or help to others; meddlesome.
Review
Pablum (noun)
Answer
Pablum (noun)
Trite, insipid, or simplistic writing, speech, or conceptualization.
Originally, pablum was the trademark name for a soft, bland, mushy, easy-to-digest cereal developed for infants and invalids in the 1930s.
Pablum was derived from the related word pabulum, which can refer to a nourishing substance or to insipid intellectual nourishment.
A wonderful synonym for pablum is pap. Like pablum, pap also originally referred to soft food for infants. “That white paper from the think tank is just intellectual pap.”
Review
Paean (noun)
Answer
Paean (noun)
1. A joyous song or hymn of praise, thanksgiving, or triumph.
2. Speech or writing that expresses enthusiastic praise.
In ancient Greece, a paean was a hymn of invocation or thanksgiving to Apollo or another Greek deity. Today, the word is used more generally to refer to a hymn of praise or thanksgiving or to speech or writing that expresses praise.
Paean is often used for critical acclaim of books, plays, and movies, as in: “The play received a paean from the usually negative critics.”
Review
Palaver (noun)
Answer
Palaver (noun)
1. Profuse and idle chit-chat; chatter; empty talk; nonsense.
2. Flattery and sweet talk used to persuade.
“The high school English teacher, annoyed at the incessant chattering in class, said, ‘Let’s put an end to this palaver and start our discussion of Macbeth.’”
Review
Panacea (n)
Answer
Panacea (n)
a solution or remedy for all difficulties or diseases.
"the panacea for all corporate ills"
a solution or remedy for all difficulties or diseases.
"the panacea for all corporate ills"
Review
Panegyric (noun)
Answer
Panegyric (noun)
Formal or elaborate praise; specifically, a formal speech or writing that offers praise.
Panegyric refers to lofty, formal praise, such as that given in a speech. For example: “The general’s panegyric for his fallen soldiers moved everyone to tears.”
Synonyms and words related to panegyric include accolade, commendation, homage, tribute, and encomium.
Panegyric is derived from two Greek roots: pan (“all”) and agora (“marketplace”). The combination of the two yields the image of a formal speech of praise delivered to all those assembled in a public meeting place.
Review
Parricide (noun)
Answer
Parricide (noun)
The murder of a parent or close relative.
English has many words containing this root, including suicide, homicide, matricide, patricide, infanticide, regicide, and the target word here, parricide.
Review
Patrician (noun/adjective)
Answer
Patrician (noun/adjective)
noun:
1. Someone of refined upbringing, manners, and taste.
2. An aristocrat; a person of high rank or social class.
adjective: People or things that have the characteristics of the upper class.
“The city’s patricians used to have most of the money and power, but the growth of the middle class has all but ended that era in history.”
“Her patrician tastes in music and dining were apparent from her frequent trips to the opera, the symphony orchestra, and only the finest restaurants in town.”
The patricians were members of the original aristocratic families of ancient Rome. In contrast to the patrician class was the plebeian or working class. Today, plebeian is used as an antonym for patrician to refer to something that is common, lower class, or vulgar.
Review
Peckish (adjective)
Answer
Peckish (adjective)
1. Somewhat hungry.
2. Irritable, touchy.
Review
Perdition (noun)
Answer
Perdition (noun)
Loss of the soul; eternal damnation; hell; utter ruin.
Review
Perfidious (adjective)
Answer
Perfidious (adjective)
Treacherous, disloyal, and deceitful.
"The perfidious soldier switched sides during the war, revealing his commanding general’s strategy to the enemy."
Perfidious literally means “through or beyond the limits of faith.” A trusted friend who stabs you in the back goes beyond the limits of your faith.
Review
Pernicious (adjective)
Answer
Pernicious (adjective)
Exceedingly harmful or destructive; deadly.
Review
Perspicacious (adjective)
Answer
Perspicacious (adjective)
Having or showing keen mental perception.
Synonyms and related words for perspicacious include acute, astute, discerning, penetrating, sagacious, and sapient.
Review
Philatelist (noun)
Answer
Philatelist (noun)
A person or studies or collects stamps.
Review
Philippic (noun)
Answer
Philippic (noun)
A bitter verbal attack; a rant filled with harsh, cruel language.
The original philippics were a series of speeches by the great Athenian orator Demosthenes. In these speeches, Demosthenes denounced King Philip of Macedon and warned his fellow Athenians of Philip’s political ambitions.
Synonyms:
Invective is a noun that refers to a vehement or violent denunciation; a railing accusation, usually bitter and sarcastic, as in “The prisoner hurled a stream of invectives at the judge,
jury, and prosecutors as he was led away in chains.”
Vituperation is a synonym for invective that refers to a violent denunciation or verbal abuse or castigation. It’s often heard in its adjective form, vituperative.
A diatribe is a bitter, sharply abusive denunciation, attack, or criticism. For example: “The increasingly bitter diatribes against the horrific boss led to his resignation.
A tirade is a long, vehement speech or bitter denunciation. For example, "After finding cigarette butts and ash in the customers’ food, the health inspector launched into a 20-minute tirade against smoking in the restaurant’s kitchen.”
A harangue can be a noun that means a scolding or a long and intense verbal attack. Harangue can also be used as a verb meaning to deliver such a verbal attack, as in “His mother constantly harangues him about his messy room.”
Review
Philistine (noun)
Answer
Philistine (noun)
A person who is uninterested in intellectual pursuits and indifferent or hostile to artistic and cultural values.
Review
Phlegmatic (adjective)
Answer
Phlegmatic (adjective)
Showing little emotion; not easily excited to action.
Phlegmatic means “unemotional,” which can be both a positive and a negative attribute.
Review
Pillory (noun)
Answer
Pillory (noun)
To expose to (often public) ridicule, abuse, and scorn; to criticize harshly.
From the Middle Ages up until the early 1800s in some places, pillory referred to a device used for public punishment: a wooden or metal frame with holes into which the head and hands of a person accused of a crime would be locked.
Review
Piquant (adjective)
Answer
Piquant (adjective)
1. Agreeably pungent or sharp in the taste or flavor; pleasantly biting or tart; spicy.
2. Agreeably stimulating and engagingly provocative.
3. Interesting, charming, attractive.
Piquant comes from the French word piquer, meaning “to prick or sting,” and is related to the English word pike, a long, spear-like weapon.
Review
Pithy (adjective)
Answer
Pithy (adjective)
Language that is short and terse but meaningful.
Both pithy and laconic refer to language that is brief and succinct, but pithy implies the added meaning of language that is meaningful and powerful. For example: “In direct contrast to the bombastic, long-winded arguments of the prosecuting attorney, the defense attorney’s pithy arguments won the case.”
Pithy comes from pith, which is the soft, spongy center of the stem of most flowering plants.
Review
Pontificate (verb)
Answer
Pontificate (verb)
To speak or express opinions in a pompous or dogmatic way.
Review
Prescient (adjective)
Answer
Prescient (adjective)
Perceiving the significance of events before they happen.
Ex. A prescient warning from historians.
Ex. A prescient warning from historians.
Review
Procrustean (adjective)
Answer
Procrustean (adjective)
Tending to produce conformity by arbitrary, ruthless, or violent means.
Even though the student’s poem unanimously won the all-county writing contest, the procrustean English teacher gave her an F for failing to dot the i in her name.
Greek mythology, Procrustes was a mythical bandit of Attica who would waylay hapless travelers and attempt to fit them to his iron bed. If travelers were too long for the bed, he’d cut off their feet. If they were too short, he’d stretch them out.
Review
Profligate
Answer
Profligate
Someone who is given to wildly extravagant and grossly self-indulgent behavior.
Review
Promethean (adjective)
Answer
Promethean (adjective)
Daringly original or creative; boldly inventive.
"the Promethean scientist who unlocked the mysteries of the cosmos"
"the Promethean scientist who unlocked the mysteries of the cosmos"
Review
Propitiate (verb)
Answer
Propitiate (verb)
To appease; to make favorably inclined; to regain the favor of someone.
Propitiate is often used in religious contexts, as in: The priest propitiated the gods by sacrificing a fatted calf.
Synonyms for propitiate include mollify, dulcify, conciliate, and placate.
Review
Prosaic (adjective)
Answer
Prosaic (adjective)
1. Dull, lacking in imagination, matter-of-fact.
2. Commonplace, everyday, ordinary.
Like insipid and vapid, prosaic can mean “dull,” but it emphasizes dullness as a result of lack of imagination. For example: “Often, science writing can be prosaic, simply delivering information in a lifeless, unimaginative, ‘just the facts, ma’am’ style.”
“The seemingly prosaic lives of our immigrant ancestors, who worked tirelessly in the steel mills, belie the heroic sacrifices they made for their descendants.”
Review
Protean (adjective)
Answer
Protean (adjective)
Able to take many forms or do many different things; versatile.
Review
Puerile (adjective)
Answer
Puerile (adjective)
Juvenile, childishly silly, foolish.
“After sitting on a whoopee cushion and hearing inappropriate noises made by his
students, the teacher called for an end to the puerile humor, warning of severe consequences.”
Puerile comes from the Latin puer, meaning “boy or male child,” and as we
all know, boys can certainly be silly.
Review
Pusillanimous (adjective)
Answer
Pusillanimous (adjective)
Cowardly; lacking courage or resolution; fainthearted.
Review
Quark (noun)
Answer
Quark (noun)
An elementary subatomic particle proposed as the fundamental unit of matter.
Review
Querulous (adj.)
Answer
Querulous (adj.)
Full of complaints; complaining in an annoyed way.
Querulous can be used to describe a person or his or her manner or actions. For example: “Her normally positive teenage daughter became querulous when she stayed up too late, complaining about her teachers, her social life, and her siblings.”
Review
Quiescent (adjective)
Answer
Quiescent (adjective)
Tranquilly at rest, inactive, still, quiet, or motionless.
Review
Quisling (noun)
Answer
Quisling (noun)
A traitor who aids an invading and/or occupying enemy force, often serving later in the puppet government.
Review
Quixotic (adjective)
Answer
Quixotic (adjective)
Romantically impractical or impulsive.
Review
Quotidian (adjective)
Answer
Quotidian (adjective)
Daily, customary, ordinary, usual.
Quotidian describes the mundane, unexciting things that we all do routinely, such as washing the dishes, making the bed, and going to work.
Synonyms for quotidian include everyday, garden variety, frequent, common, and routine.
"the car sped noisily off through the quotidian traffic"
"the car sped noisily off through the quotidian traffic"
Review
Rapacious (adj.)
Answer
Rapacious (adj.)
Aggressively and excessively greedy or grasping; predatory.
Rapacious doesn’t just mean aggressive; it has the added connotation of greedy and grasping behavior. Here’s a sentence that puts the word in context: “The rapacious company bought up all its smaller competitors until it had the monopoly on lollipops in North America.”
Synonyms for rapacious include ravenous, voracious, and avaricious. Use rapacious when you want to emphasize the greedy, devouring nature of aggression.
Review
Recondite (adjective)
Answer
Recondite (adjective)
Difficult to understand.
Something that perhaps goes beyond erudite or scholarly may be described as recondite.
Review
Salubrious (adjective)
Answer
Salubrious (adjective)
Conducive or favorable to health or well-being; wholesome.
Review
Salutary (adjective)
Answer
Salutary (adjective)
Producing a beneficial effect; remedial.
Review
Sangfroid (noun)
Answer
Sangfroid (noun)
Coolness and composure, especially in trying circumstances.
Review
Saturnalia (noun)
Answer
Saturnalia (noun)
A celebration marked by unrestrained revelry and, often, promiscuity and excessive drinking.
Review
Saturnine (adjective)
Answer
Saturnine (adjective)
Melancholy, sluggish, gloomy.
(of a person or their manner) gloomy.
"a saturnine temperament"
Review
Scabrous (adj.)
Answer
Scabrous (adj.)
1. Scabby, blotchy, and scaly.
2. Rough to the touch.
3. Indecent, shocking, scandalous.
Although scabrous carries all three meanings listed above, it’s
often used to describe indecent, risqué, and obscene language and behavior. For example: “The intimate details of the late celebrity’s scabrous diary shocked his family and ignited a scandal.” Synonyms and related words for this sense of scabrous include salacious, libidinous, and lascivious.
Scabrous originally came from the Latin adjective scaber, meaning “rough, scaly”; this word, in turn, was related to the Latin verb scabo, meaning “to scratch or scrape.” Not surprisingly, scabrous is also related to scab and scabies.
Review
Schadenfreude (noun)
Answer
Schadenfreude (noun)
Satisfaction, pleasure, or malicious joy at someone else’s misfortune.
"a business that thrives on schadenfreude"
"a business that thrives on schadenfreude"
Review
Schism (noun)
Answer
Schism (noun)
A division among the members of a group into opposing factions because of a disagreement.
Synonyms and related words for schism include split, rift, division, parting of the ways, falling-out, fracture, rupture, fissure, breach, and cleft.
Review
Scullion (noun)
Answer
Scullion (noun)
a servant assigned the most menial kitchen tasks.
Review
Sedulous (adjective)
Answer
Sedulous (adjective)
Diligent in application or in the pursuit of something; persevering; constant in effort.
Synonyms for sedulous include diligent, assiduous, persistent, tenacious, and pertinacious.
Review
Sesquipedalian (adjective)
Answer
Sesquipedalian (adjective)
1. Given to the overuse of long words.
2. Long and ponderous, polysyllabic.
Sesquipedalian comes from the Latin sesqui- (“half as much again”) and ped("foot").
Review
Shibboleth (noun)
Answer
Shibboleth (noun)
A test word, phrase, or custom used to distinguish one group from another.
Review
Sisyphean (adjective)
Answer
Sisyphean (adjective)
Endlessly laborious and futile.
The word Sisyphean comes from the Greek myth of Sisyphus.
Review
Skulduggery (n.)
Answer
Skulduggery (n.)
Devous, deceitful behavior; underhanded dealings.
Review
Sobriquet (noun)
Answer
Sobriquet (noun)
A nickname, usually a humorous or affectionate one.
Review
Solipsism (noun)
Answer
Solipsism (noun)
1. The philosophy that one has no valid reason for believing that anything exists except oneself.
2. An extreme preoccupation with one’s own feelings and thoughts.
Solipsism was coined in 1871 from two Latin words: solus, meaning “alone,” and ipse, meaning “self.” It’s commonly used in reference to an extremely egocentric person.
Review
Somniloquy (noun)
Answer
Somniloquy (noun)
Sleep talking.
Review
Specious (adjective)
Answer
Specious (adjective)
Having the ring of truth or plausibility but actually fallacious.
Specious is an adjective that describes the type of argument a sophist might deliver: one that seems plausible on the surface but is fallacious underneath.
Specious comes from the Latin speciosus, meaning “good looking,” which came from species, meaning “appearance.” Thus, a specious argument is one that “looks good” on the surface but isn’t sound. Specious is also related to the Latin root spec, meaning “look.”
Review
Splenetic (adjective)
Answer
Splenetic (adjective)
Bad-tempered, irritable, or spiteful.
The word splenetic is actually related to spleen, which was considered the seat of moroseness and bad temper in medieval physiology.
English has a wide variety of synonyms for splenetic, including bristly, prickly, crabby, cranky, crotchety, cantankerous, irascible (easily provoked), testy (irritated by small annoyances), and dyspeptic (gloomy, sullen, and irritable).
Review
Spurious (adjective)
Answer
Spurious (adjective)
Not genuine, authentic, or true; false.
Spurious is often used as a synonym for specious, but it actually has a slightly different connotation. Like specious, spurious refers to something that is false or counterfeit, including an argument or claim. However, as we saw, a specious argument seems plausible on the surface; in contrast, a spurious argument is immediately recognized as false.
Review
Stoic (adjective)
Answer
Stoic (adjective)
Seemingly indifferent to or unaffected by joy, grief, pleasure or pain.
phlegmatic “implies a temperament or constitution in which emotion is hard to arouse.” Thus, phlegmatic carries the suggestion of inborn or natural lack of emotion.
Stoic, however, suggests restraint that has been gained through self-discipline and as a matter of principle.
Review
Stolid (adjective)
Answer
Stolid (adjective)
Having or expressing little or no sensibility; unemotional.
it also “implies heavy, dull, obtuse impassivity or apathy” and suggests “impassive, mechanical, plodding, unquestioning adherence to routine.”
Review
Stultify (verb)
Answer
Stultify (verb)
1. To cause to lose interest; to cause to feel dull and not alert.
2. To render useless or ineffectual.
Review
Supercilious (adjective)
Answer
Supercilious (adjective)
Feeling or showing haughty disdain; displaying arrogant pride, even scorn.
Supercilious often describes people or facial expressions.
Wonderfully vivid and descriptive synonyms and related words for supercilious are legion in English, including arrogant, uppity, haughty, pompous, priggish, pretentious, prideful, patronizing, disdainful, condescending, swaggering, lofty, lordly, high and mighty, highfalutin, sniffy, snooty, and snotty.
"a supercilious lady's maid"
"a supercilious lady's maid"
Review
Susurration (noun)
Answer
Susurration (noun)
An indistinct whispering or rustling sound; a murmur
Review
Sycophant (noun)
Answer
Sycophant (noun)
A servile, self-seeking flatterer.
English includes some wonderfully vivid synonyms for sycophants, including grovelers, backscratchers, bootlickers, toadies, and lickspittles.
Review
Temerity (noun)
Answer
Temerity (noun)
Reckless boldness; rashness; foolhardy disregard of danger.
Review
Tendentious (adjective)
Answer
Tendentious (adjective)
Marked by or favoring a particular point of view; showing a definite tendency, bias, or purpose; partisan.
"a tendentious reading of history"
"a tendentious reading of history"
Review
Timorous (adjective)
Answer
Timorous (adjective)
Fearful or timid.
Both timorous and timid come from the Latin verb timeo, meaning “to be afraid.”
Review
Toothsome (adjective)
Answer
Toothsome (adjective)
Delicious; sexually attactive.
Review
Toponym (noun)
Answer
Toponym (noun)
1. A place-name.
2. A word named after a place.
Review
Torpid (adjective)
Answer
Torpid (adjective)
Slow, sluggish, lethargic, dull, benumbed.
Torpor and torpid come from the Latin word torpeo, meaning “to be numb, inactive, or dull.”
Review
Torpor (noun)
Answer
Torpor (noun)
Sluggishness; a state of mental or physical inactivity; lethargy, apathy.
Review
Treacle (n.)
Answer
Treacle (n.)
Cloying, sickly-sweet speech or sentiment.
Treacle refers to excessively sweet sentiment, as seen in overly romantic movies or grocery-store greeting cards. Treacle can also refer to molasses or golden syrup, which is a thick, sweet mixture of molasses, corn syrup, and sugar used in cooking.
The adjective form of treacle is treacly. Synonyms and related words include cloying and saccharine.
Review
Trenchant (adjective)
Answer
Trenchant (adjective)
Forceful and clear; penetrating, keen, and incisive.
Review
Truckle (verb)
Answer
Truckle (verb)
1. To submit; to be servile and submissive.
2. To fawn; to curry favor by flattering.
Truckle is often followed by its collocate to in such phrases as “truckle to those in power” and “truckle to another country’s demands.”
Review
Truculent (adjective)
Answer
Truculent (adjective)
Cruel, savage, brutal, and fierce; disposed to fighting; scathing and brutally harsh, often referring to verbal criticism.
Example: They behaved in the most high-handed, brutal and truculent manner.
Review
Turbid (adjective)
Answer
Turbid (adjective)
1. Muddy, thick, or opaque with sediment; obscured; clouded.
2. Confused, muddled, disordered.
Turbid is often used to describe roiled, muddy water or liquid that’s heavy, thick, and dense, as in: “The turbid river, full of mud and debris from the flood, made it nearly impossible for the rescure teams to recover the missing.”
Turbid includes the root turb, which comes from the Latin word turba, meaning “turmoil or confusion.” The root can also carry the connotation of “spinning and whirling.” Other words that share the turb root include turbulent, disturb, perturb, imperturbable, and turbine.
Review
Turgid (adjective)
Answer
Turgid (adjective)
Swollen, distended, puffy.
Turgid can refer to physical swollenness, as in: “The disease had ravaged his body, leading to swollen limbs and turgid facial features."
“The love song’s turgid lyrics and hackneyed expressions made it unpopular with listeners.”
Review
Turpitude (noun)
Answer
Turpitude (noun)
Baseness, depravity, or debauchery.
"acts of moral turpitude"
"acts of moral turpitude"
Review
Tyro (noun)
Answer
Tyro (noun)
A beginner or novice.
“Under the legendary fly-fishing guide's expert mentoring, even a fly-fishing tyro like me would be able to land a trout in this stream.”
Tyro can also be used as an adjective, as in: “The tyro teacher knew her subject but lacked classroom management skills; her students were completely unruly when the principal walked in for her first observation.”
Synonyms and related words for tyro include beginner, rookie, neophyte, abecedarian, tenderfoot, and greenhorn.
Review
Unctuous (adjective)
Answer
Unctuous (adjective)
Characterized by affected, exaggerated, or insincere earnestness.
Unctuous comes from the Latin unctus, meaning “anointed with oil.”
A wonderful synonym for unctuous that’s a little shorter and more down to earth is smarmy, as in “The smarmy aide thought that his constant blandishments would butter up the congressman and eventually lead to an appointment.”
Review
Vapid (adjective)
Answer
Vapid (adjective)
Completely lacking in zest, spirit, animation, and liveliness.
Vapid comes from the Latin vapidus, meaning “that has exhaled its vapor.” Vapid was originally used in English in a literal sense to describe stale beverages that had lost their flavor, or vapor.
If you want to emphasize dullness due to a lack of taste or interest, insipid might be the right choice. If, however, you want to emphasize dullness due to lack of zest, spirit, and life, vapid might work better.
For example, a meal can be insipid but not vapid. A conversation can be either, depending on what aspect of its supreme dullness you want to call attention to.
Review
Venal (adjective)
Answer
Venal (adjective)
Open to corruption; capable of being bought through bribery.
Venal is derived from the Latin venum, meaning “something for sale.” Related English words include vendor and vending.
Review
Vernacular (noun)
Answer
Vernacular (noun)
Form of a language spoken by the common people, as opposed to the learned and literary.
Review
Vilify (verb)
Answer
Vilify (verb)
To attack someone’s reputation with strong or abusive criticism; to malign.
Synonyms and related words for vilify are numerous, including backbite, malign, slander, slur, libel, defame, disparage, denigrate, knock down, put down, tear down, slam, pan, besmirch, smear, and sully.
Review
Virulent (adjective)
Answer
Virulent (adjective)
1. Extremely infectious, malignant, poisonous, or deadly.
2. Bitterly hostile, antagonistic, or spiteful; hateful.
Review
Weltschmerz (noun)
Answer
Weltschmerz (noun)
Sadness over the evils of the world.
Review
Wheedle (verb)
Answer
Wheedle (verb)
To attempt to persuade with beguiling flattery and smooth talking.
“The teenage girl wheedled her father into letting her drive his Porsche 911 with a few crocodile tears, a sob story, and the seemingly sincere assurance that he was ‘the best dad in the world.’”
Wheedle brings to mind the behavior of the snake-oil salesmen, charlatans, hucksters, and mountebanks.
Common synonyms for wheedle include cajole and coax.
Review
Xenophobia (noun)
Answer
Xenophobia (noun)
An unreasonable hatred or fear of foreigners or strangers; a fear of that which is foreign or strange.
Review
Zeitgeist (noun)
Answer
Zeitgeist (noun)
The spirit, attitude, or general outlook of a specific period; the moral, cultural, and intellectual climate of an era.
Group Theory 108 cards New: 0Learning: 0Review: 108Relearning: 0Unknown: 0
Group Theory
108 cards
Review
\(\text{Inn(G)} \) is a [...] of \(\text{Aut}(G) \)
Answer
\(\text{Inn(G)} \) is a normal subgroup of \(\text{Aut}(G) \)
Review
A [...] on a set \(S\) consists of a group \(F\) and a function \(\iota: S \to F\) such that for every group \(G\) and function \(\phi: S \to G\) there exists a unique homomorphism \(\Phi: F \to G\) such that \(\phi = \iota \circ \Phi \)
Answer
A free group on a set \(S\) consists of a group \(F\) and a function \(\iota: S \to F\) such that for every group \(G\) and function \(\phi: S \to G\) there exists a unique homomorphism \(\Phi: F \to G\) such that \(\phi = \iota \circ \Phi \)
Review
A \(p\)-Sylow subgroup of a finite group is a subgroup \(P\leq G\) which is a \(p\)-group is such that [...]. Equivalently, if \(|G| = p^am\) with \( (p, m) = 1 \), then \(P\) is a subgroup of order \(p^a \)
Answer
A \(p\)-Sylow subgroup of a finite group is a subgroup \(P\leq G\) which is a \(p\)-group is such that \(|G:P| \) is prime to \(p\) . Equivalently, if \(|G| = p^am\) with \( (p, m) = 1 \), then \(P\) is a subgroup of order \(p^a \)
Review
A \(p\)-Sylow subgroup of a finite group is a subgroup \(P\leq G\) which is a \(p\)-group is such that \(|G:P| \) is prime to \(p\) . Equivalently, if \(|G| = p^am\) with \( (p, m) = 1 \), then \(P\) is a subgroup of order [...]
Answer
A \(p\)-Sylow subgroup of a finite group is a subgroup \(P\leq G\) which is a \(p\)-group is such that \(|G:P| \) is prime to \(p\) . Equivalently, if \(|G| = p^am\) with \( (p, m) = 1 \), then \(P\) is a subgroup of order \(p^a \)
Review
A finite group \(G\) is [...] if its composition factors are abelian.
Answer
A finite group \(G\) is solvable if its composition factors are abelian.
Review
A finite p-group is isomorphic to a [...] if and only if it is abelian
Answer
A finite p-group is isomorphic to a product of cyclic groups if and only if it is abelian
Review
A finite p-group is isomorphic to a product of cyclic groups if and only if it is [...]
Answer
A finite p-group is isomorphic to a product of cyclic groups if and only if it is abelian
Review
A fixed point of an action by \(G\) on \(X\) is an \(x \in X\) such that [...].
Answer
A fixed point of an action by \(G\) on \(X\) is an \(x \in X\) such that \(G_x =G\).
Review
A free group on a set \(S\) consists of a group \(F\) and a function \(\iota: S \to F\) such that for every group \(G\) and function \(\phi: S \to G\) there exists a unique homomorphism \(\Phi: F \to G\) such that [...]
Answer
A free group on a set \(S\) consists of a group \(F\) and a function \(\iota: S \to F\) such that for every group \(G\) and function \(\phi: S \to G\) there exists a unique homomorphism \(\Phi: F \to G\) such that \(\phi = \iota \circ \Phi \)
Review
A group \(G\) is torsion if [...]
Answer
A group \(G\) is torsion if \(G_{tors} = G\)
Review
A group \(G\) is solvable if it admits a finite chain of subgroups
[...]
such that each quotient \(G_k/G_{k-1} \) is abelian
[...]
such that each quotient \(G_k/G_{k-1} \) is abelian
Answer
A group \(G\) is solvable if it admits a finite chain of subgroups
\(1 = G_0 \unlhd G_1 \unlhd \dots \unlhd G_s = G \)
such that each quotient \(G_k/G_{k-1} \) is abelian
\(1 = G_0 \unlhd G_1 \unlhd \dots \unlhd G_s = G \)
such that each quotient \(G_k/G_{k-1} \) is abelian
Review
A group \(G\) is solvable if it admits a finite chain of subgroups
\(1 = G_0 \unlhd G_1 \unlhd \dots \unlhd G_s = G \)
such that each [...]
\(1 = G_0 \unlhd G_1 \unlhd \dots \unlhd G_s = G \)
such that each [...]
Answer
A group \(G\) is solvable if it admits a finite chain of subgroups
\(1 = G_0 \unlhd G_1 \unlhd \dots \unlhd G_s = G \)
such that each quotient \(G_k/G_{k-1} \) is abelian
\(1 = G_0 \unlhd G_1 \unlhd \dots \unlhd G_s = G \)
such that each quotient \(G_k/G_{k-1} \) is abelian
Review
A group G is nilpotent if [...]
Answer
A group G is nilpotent if there exists a \(c\) such that \(Z_c(G) = G\)
Review
A group of order \(p^{\alpha}\) for some \(\alpha \geq 1\) is called a [...].
Answer
A group of order \(p^{\alpha}\) for some \(\alpha \geq 1\) is called a p-group.
Review
A subgroup \(H \leq G\) is [...] iff it is the kernel of some homomorphism
Answer
A subgroup \(H \leq G\) is normal iff it is the kernel of some homomorphism
Review
A subgroup \(H \leq G\) is normal iff it is [...]
Answer
A subgroup \(H \leq G\) is normal iff it is the kernel of some homomorphism
Review
A subgroup of index 2 is [...]
Answer
A subgroup of index 2 is normal
Review
A composition series for a group \(G\) is a finite chain of subgroups
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) [...]
(2) The quotient \(M_k / M_{k-1} \) is a simple group
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) [...]
(2) The quotient \(M_k / M_{k-1} \) is a simple group
Answer
A composition series for a group \(G\) is a finite chain of subgroups
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) \(M_{k-1}\) is a normal subgroup of \( M_k \)
(2) The quotient \(M_k / M_{k-1} \) is a simple group
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) \(M_{k-1}\) is a normal subgroup of \( M_k \)
(2) The quotient \(M_k / M_{k-1} \) is a simple group
Review
A composition series for a group \(G\) is a finite chain of subgroups
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) \(M_{k-1}\) is a normal subgroup of \( M_k \)
(2) [...]
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) \(M_{k-1}\) is a normal subgroup of \( M_k \)
(2) [...]
Answer
A composition series for a group \(G\) is a finite chain of subgroups
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) \(M_{k-1}\) is a normal subgroup of \( M_k \)
(2) The quotient \(M_k / M_{k-1} \) is a simple group
\( \{e \} = M_0 \leq M_2 \leq \dots \leq M_{r-1} \leq M_r = G, r \geq 0 \)
such that
(1) \(M_{k-1}\) is a normal subgroup of \( M_k \)
(2) The quotient \(M_k / M_{k-1} \) is a simple group
Review
A split extension is such an extension, together with [...] such that \(K' \to G/H', \quad x \mapsto xH' \) is an isomorphism.
Answer
A split extension is such an extension, together with \(K' \leq G \) such that \(K' \to G/H', \quad x \mapsto xH' \) is an isomorphism.
Review
A split extension is such an extension, together with \(K' \leq G \) such that [...] is an isomorphism.
Answer
A split extension is such an extension, together with \(K' \leq G \) such that \(K' \to G/H', \quad x \mapsto xH' \) is an isomorphism.
Review
An [...] if and only if it is cyclic of prime order
Answer
An abelian group is simple if and only if it is cyclic of prime order
Review
An abelian group is simple if and only if [...]
Answer
An abelian group is simple if and only if it is cyclic of prime order
Review
An action is [...] if it has exactly one orbit.
Answer
An action is transitive if it has exactly one orbit.
Review
Any finite abelian group is a product of [...]
Answer
Any finite abelian group is a product of its Sylow subgroups
Review
Consider the free group \(F_G\) on \(G\). By the universal property of free groups, there exists a unique group homomorphism [...] whose restriction to \(G\) is the identity map. Let \(K\) be the kernel of this homomorphism. Then, \(K\) is normal in \(F_G\), therefore is equal to its normal closure, so \(\langle G | K \rangle = F_G/K \). Since the identity map is surjective, \(\varphi\) is also surjective, so by the First Isomorphism Theorem, \(\langle G | K \rangle \cong \text{im}\varphi = G \)
Answer
Consider the free group \(F_G\) on \(G\). By the universal property of free groups, there exists a unique group homomorphism \(\varphi: F_G \to G\) whose restriction to \(G\) is the identity map. Let \(K\) be the kernel of this homomorphism. Then, \(K\) is normal in \(F_G\), therefore is equal to its normal closure, so \(\langle G | K \rangle = F_G/K \). Since the identity map is surjective, \(\varphi\) is also surjective, so by the First Isomorphism Theorem, \(\langle G | K \rangle \cong \text{im}\varphi = G \)
Review
Consider the free group \(F_G\) on \(G\). By the universal property of free groups, there exists a unique group homomorphism \(\varphi: F_G \to G\) whose restriction to \(G\) is the identity map. Let \(K\) be the kernel of this homomorphism. Then, \(K\) is [...], so \(\langle G | K \rangle = F_G/K \). Since the identity map is surjective, \(\varphi\) is also surjective, so by the First Isomorphism Theorem, \(\langle G | K \rangle \cong \text{im}\varphi = G \)
Answer
Consider the free group \(F_G\) on \(G\). By the universal property of free groups, there exists a unique group homomorphism \(\varphi: F_G \to G\) whose restriction to \(G\) is the identity map. Let \(K\) be the kernel of this homomorphism. Then, \(K\) is normal in \(F_G\), therefore is equal to its normal closure, so \(\langle G | K \rangle = F_G/K \). Since the identity map is surjective, \(\varphi\) is also surjective, so by the First Isomorphism Theorem, \(\langle G | K \rangle \cong \text{im}\varphi = G \)
Review
Consider the free group \(F_G\) on \(G\). By the universal property of free groups, there exists a unique group homomorphism \(\varphi: F_G \to G\) whose restriction to \(G\) is the identity map. Let \(K\) be the kernel of this homomorphism. Then, \(K\) is normal in \(F_G\), therefore is equal to its normal closure, so \(\langle G | K \rangle = F_G/K \). Since the identity map is surjective, \(\varphi\) is also surjective, so by the First Isomorphism Theorem,[...]
Answer
Consider the free group \(F_G\) on \(G\). By the universal property of free groups, there exists a unique group homomorphism \(\varphi: F_G \to G\) whose restriction to \(G\) is the identity map. Let \(K\) be the kernel of this homomorphism. Then, \(K\) is normal in \(F_G\), therefore is equal to its normal closure, so \(\langle G | K \rangle = F_G/K \). Since the identity map is surjective, \(\varphi\) is also surjective, so by the First Isomorphism Theorem, \(\langle G | K \rangle \cong \text{im}\varphi = G \)
Review
Every [...] has a composition series.
Answer
Every finite group has a composition series.
Review
Every \(p\) group has a [...]
Answer
Every \(p\) group has a non-trivial center
Review
Every finitely generated [...] is finite
Answer
Every finitely generated torsion abelian group is finite
Review
Every finitely generated abelian group \(G\) is isomorphic to one of the form
\(G \cong F \times \mathbb{Z}^r, \quad |F| < \infty \)
or
[...]
\(G \cong F \times \mathbb{Z}^r, \quad |F| < \infty \)
or
[...]
Answer
Every finitely generated abelian group \(G\) is isomorphic to one of the form
\(G \cong F \times \mathbb{Z}^r, \quad |F| < \infty \)
or
\( \mathbb{Z}^r \)
\(G \cong F \times \mathbb{Z}^r, \quad |F| < \infty \)
or
\( \mathbb{Z}^r \)
Review
Every finitely generated abelian group \(G\) is isomorphic to one of the form
[...]
or
\( \mathbb{Z}^r \)
[...]
or
\( \mathbb{Z}^r \)
Answer
Every finitely generated abelian group \(G\) is isomorphic to one of the form
\(G \cong F \times \mathbb{Z}^r, \quad |F| < \infty \)
or
\( \mathbb{Z}^r \)
\(G \cong F \times \mathbb{Z}^r, \quad |F| < \infty \)
or
\( \mathbb{Z}^r \)
Review
Every finitely generated torsion abelian group is [...]
Answer
Every finitely generated torsion abelian group is finite
Review
For a finite group \(G\) with \( p \mid |G| \), we have
\( \{g \in G | \exists k \geq 0, |g| = p^k \} =\) [...]
\( \{g \in G | \exists k \geq 0, |g| = p^k \} =\) [...]
Answer
For a finite group \(G\) with \( p \mid |G| \), we have
\( \{g \in G | \exists k \geq 0, |g| = p^k \} =\) \( \bigcup_{P \in \text{Syl}_p(G)} P \)
\( \{g \in G | \exists k \geq 0, |g| = p^k \} =\) \( \bigcup_{P \in \text{Syl}_p(G)} P \)
Review
For any subgroup \(H\) of a group \(G\), the quotient group \(N_G(H)/C_G(H) \) is isomorphic to a subgroup of [...]. In particular, \(G/Z(G)\) is isomorphic to a subgroup of [...]
Answer
For any subgroup \(H\) of a group \(G\), the quotient group \(N_G(H)/C_G(H) \) is isomorphic to a subgroup of \(Aut(H)\) . In particular, \(G/Z(G)\) is isomorphic to a subgroup of \(Aut(G) \)
Review
For each fixed \(g \in G\) we get a map \(\sigma_g\) defined by
\( \sigma_g: A \to A \)
\( \sigma_g(a) = g \cdot a\)
Name two important facts about this map
\( \sigma_g: A \to A \)
\( \sigma_g(a) = g \cdot a\)
Name two important facts about this map
Answer
For each fixed \(g \in G\) we get a map \(\sigma_g\) defined by
\( \sigma_g: A \to A \)
\( \sigma_g(a) = g \cdot a\)
Name two important facts about this map
1. for each fixed \(g \in G\), \(\sigma_g\) is a permutation of \(A\)
2. the map from \(G\) to \(S_A\) defined by \(g \mapsto \sigma_g\) is a homormorphism
\( \sigma_g: A \to A \)
\( \sigma_g(a) = g \cdot a\)
Name two important facts about this map
1. for each fixed \(g \in G\), \(\sigma_g\) is a permutation of \(A\)
2. the map from \(G\) to \(S_A\) defined by \(g \mapsto \sigma_g\) is a homormorphism
Review
If \(\varphi: G \to H\) is a homomorphism of groups, then [...] and \(G /\text{ker}\varphi \cong \varphi(G)\)
Answer
If \(\varphi: G \to H\) is a homomorphism of groups, then \(\text{ker}\varphi \unlhd G\) and \(G /\text{ker}\varphi \cong \varphi(G)\)
Review
If \(\varphi: G \to H\) is a homomorphism of groups, then \(\text{ker}\varphi \unlhd G\) and [...]
Answer
If \(\varphi: G \to H\) is a homomorphism of groups, then \(\text{ker}\varphi \unlhd G\) and \(G /\text{ker}\varphi \cong \varphi(G)\)
Review
If \(|G| = p^2\) for some prime \(p\), then [...]
Answer
If \(|G| = p^2\) for some prime \(p\), then \(G\) is abelian
Review
If \(G = G_1 \times \dots \times G_k \) and \(g = (g_1, \dots g_k) \in G\), then \( |g|\) =[...]
Answer
If \(G = G_1 \times \dots \times G_k \) and \(g = (g_1, \dots g_k) \in G\), then \( |g|\) =\( \text{lcm}(|g_1|, \dots, |g_k| ) \)
Review
If \(G = G_1 \times \dots \times G_n \) and \(N_k \unlhd G_k \) for all \(k = 1, \dots, n\), then [...] is a normal subgroup of \(G\), and there is an isomorphism
\(G/N \cong (G_1/N_1) \times \dots \times (G_n/N_n) \)
\(G/N \cong (G_1/N_1) \times \dots \times (G_n/N_n) \)
Answer
If \(G = G_1 \times \dots \times G_n \) and \(N_k \unlhd G_k \) for all \(k = 1, \dots, n\), then \(N = N_1 \times \dots \times N_n \) is a normal subgroup of \(G\), and there is an isomorphism
\(G/N \cong (G_1/N_1) \times \dots \times (G_n/N_n) \)
\(G/N \cong (G_1/N_1) \times \dots \times (G_n/N_n) \)
Review
If \(G = G_1 \times \dots \times G_n \) and \(N_k \unlhd G_k \) for all \(k = 1, \dots, n\), then \(N = N_1 \times \dots \times N_n \) is a normal subgroup of \(G\), and there is an isomorphism
[...]
[...]
Answer
If \(G = G_1 \times \dots \times G_n \) and \(N_k \unlhd G_k \) for all \(k = 1, \dots, n\), then \(N = N_1 \times \dots \times N_n \) is a normal subgroup of \(G\), and there is an isomorphism
\(G/N \cong (G_1/N_1) \times \dots \times (G_n/N_n) \)
\(G/N \cong (G_1/N_1) \times \dots \times (G_n/N_n) \)
Review
If \(G_1, \dots, G_s\) are nilpotent, then [...]
Answer
If \(G_1, \dots, G_s\) are nilpotent, then \(G = G_1 \times \dots \times G_s\) is nilpotent
Review
If \(G/Z_G\) is cyclic, then [...]
Answer
If \(G/Z_G\) is cyclic, then \(G\) is abelian
Review
If \(G\) acts on a set \(B\) and [...] elements of \(G\) induce [...] permutations of \(B\), the action is said to be [...].
Answer
If \(G\) acts on a set \(B\) and distinct elements of \(G\) induce distinct permutations of \(B\), the action is said to be faithful.
Review
If \(G\) is a finite group, and p is the smallest [...] dividing \(|G|\), then any subgroup of index p is [...]
Answer
If \(G\) is a finite group, and p is the smallest prime dividing \(|G|\), then any subgroup of index p is normal
Review
If \(G\) is a group acting on a set \(S\) and \(s\) is some fixed element of \(S\), the stabilizer of \(s\) in \(G\) is the set
Answer
If \(G\) is a group acting on a set \(S\) and \(s\) is some fixed element of \(S\), the stabilizer of \(s\) in \(G\) is the set
\(G_s = \{g \in G | g \cdot s = s\} \)
It is also a subgroup of \(G\).
\(G_s = \{g \in G | g \cdot s = s\} \)
It is also a subgroup of \(G\).
Review
If \(G\) is a group of order \(p^{\alpha}m\), where \(p \nmid m\), then a subgroup of order \(p^{\alpha} \) is called a [...] of \(G\)
Answer
If \(G\) is a group of order \(p^{\alpha}m\), where \(p \nmid m\), then a subgroup of order \(p^{\alpha} \) is called a Sylow p-subgroup of \(G\)
Review
If \(G\) is abelian, then \(G/G_{tors}\) is [...]
Answer
If \(G\) is abelian, then \(G/G_{tors}\) is torsion free
Review
If \(G\) is an [...], then \(G_{tors}\)
is a subgroup of \(G\)
Answer
If \(G\) is an an abelian group, then \(G_{tors}\)
is a subgroup of \(G\)
Review
If \(G\) is an an abelian group, then \(G_{tors}\)
[...]
Answer
If \(G\) is an an abelian group, then \(G_{tors}\)
is a subgroup of \(G\)
Review
If \(G\) is nilpotent, then so is any [...]
Answer
If \(G\) is nilpotent, then so is any quotient group \(G/N\)
Review
If \(G\) is solvable, then then so is [...]
Answer
If \(G\) is solvable, then then so is any subgroup or quotient group of \(G\)
Review
If \(K\) is any subgroup of the group \(G\) and \(g \in G\), then \(K \cong\) [...].
Answer
If \(K\) is any subgroup of the group \(G\) and \(g \in G\), then \(K \cong\) \(gKg^{-1} \) .
Conjugate elements and conjugate subgroups have the same order.
Conjugate elements and conjugate subgroups have the same order.
Review
If \(p < q\) are primes and \(q \not\equiv 1 \mod p\), then [...]
Answer
If \(p < q\) are primes and \(q \not\equiv 1 \mod p\), then every group of order \(pq\) is a cyclic group
Review
If \(S\) is a subset of a group \(G\), then the stabilizer
\(G_S = \{g \in G | gSg^{-1} = S \} =\) [...]
Answer
If \(S\) is a subset of a group \(G\), then the stabilizer
\(G_S = \{g \in G | gSg^{-1} = S \} =\) \( N_G(S) \)
Review
Let \(\sigma, \tau \) be elements of the symmetric group \(S_n\) and suppose \(\sigma\) has cycle decomposition
\( (a_1a_2 \dots a_k)(b_1b_2\dots b_m) \)
Then \(\tau\sigma\tau^{-1} \) has cycle decomposition
\( (a_1a_2 \dots a_k)(b_1b_2\dots b_m) \)
Then \(\tau\sigma\tau^{-1} \) has cycle decomposition
Answer
Let \(\sigma, \tau \) be elements of the symmetric group \(S_n\) and suppose \(\sigma\) has cycle decomposition
\( (a_1a_2 \dots a_k)(b_1b_2\dots b_m) \)
Then \(\tau\sigma\tau^{-1} \) has cycle decomposition
\((\tau(a_1)\tau(a_2)\dots\tau(a_k)) ( \tau(b_1)\tau(b_2)\dots\tau(b_m)) \)
\( (a_1a_2 \dots a_k)(b_1b_2\dots b_m) \)
Then \(\tau\sigma\tau^{-1} \) has cycle decomposition
\((\tau(a_1)\tau(a_2)\dots\tau(a_k)) ( \tau(b_1)\tau(b_2)\dots\tau(b_m)) \)
Review
Let \(F = F(S) \) be the free group on a set \(S \). Then [...] if and only if \(S\) is finite
Answer
Let \(F = F(S) \) be the free group on a set \(S \). Then \(F\) is finitely generated if and only if \(S\) is finite
Review
Let \(F = F(S) \) be the free group on a set \(S \). Then \(F\) is finitely generated if and only if [...]
Answer
Let \(F = F(S) \) be the free group on a set \(S \). Then \(F\) is finitely generated if and only if \(S\) is finite
Review
Let \(G\) act on a finite set \(X\). We have
\(|X|\) = [...]
where \(x_1, \dots, x_k \in X\) are representatives of the orbits of the action.
\(|X|\) = [...]
where \(x_1, \dots, x_k \in X\) are representatives of the orbits of the action.
Answer
Let \(G\) act on a finite set \(X\). We have
\(|X|\) = \( \sum_{k=1}^r |G:G_{x_k}| \)
where \(x_1, \dots, x_k \in X\) are representatives of the orbits of the action.
\(|X|\) = \( \sum_{k=1}^r |G:G_{x_k}| \)
where \(x_1, \dots, x_k \in X\) are representatives of the orbits of the action.
Review
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) [...]
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) [...]
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Answer
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Review
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) [...]
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) G is nilpotent
(2) [...]
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Answer
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Review
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) [...]
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) [...]
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Answer
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Review
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) [...]
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) [...]
Answer
Let \(G\) be a finite group with \(p_1, \dots, p_s\) the distinct primes dividing its order. Then the following are equivalent:
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
(1) G is nilpotent
(2) If \(H < G\), then \(H < N_G(H) \)
(3) \( |\text{Syl}_{p_i}(G)| = 1 \) for all \(i = 1, \dots, s\)
(4) \(G \cong P_1 \times \dots \times P_s \) where \(P_i \in \text{Syl}_{p_i}(G) \)
Review
Let \(G\) be a group and let \(\phi: S \to G\) be a function. Then there exists a unique function \(\Phi: F \to G\) such that
1. [...]
2. \(\Phi(x \cdot y) = \Phi(x)\Phi(y) \quad \forall x, y \in F\)
1. [...]
2. \(\Phi(x \cdot y) = \Phi(x)\Phi(y) \quad \forall x, y \in F\)
Answer
Let \(G\) be a group and let \(\phi: S \to G\) be a function. Then there exists a unique function \(\Phi: F \to G\) such that
1. \(\Phi((s)) = \phi(s) \quad \forall s \in S \)
2. \(\Phi(x \cdot y) = \Phi(x)\Phi(y) \quad \forall x, y \in F\)
1. \(\Phi((s)) = \phi(s) \quad \forall s \in S \)
2. \(\Phi(x \cdot y) = \Phi(x)\Phi(y) \quad \forall x, y \in F\)
Review
Let \(G\) be a group and let \(\phi: S \to G\) be a function. Then there exists a unique function \(\Phi: F \to G\) such that
1. \(\Phi((s)) = \phi(s) \quad \forall s \in S \)
2. [...]
1. \(\Phi((s)) = \phi(s) \quad \forall s \in S \)
2. [...]
Answer
Let \(G\) be a group and let \(\phi: S \to G\) be a function. Then there exists a unique function \(\Phi: F \to G\) such that
1. \(\Phi((s)) = \phi(s) \quad \forall s \in S \)
2. \(\Phi(x \cdot y) = \Phi(x)\Phi(y) \quad \forall x, y \in F\)
1. \(\Phi((s)) = \phi(s) \quad \forall s \in S \)
2. \(\Phi(x \cdot y) = \Phi(x)\Phi(y) \quad \forall x, y \in F\)
Review
Let \(G\) be a group with subgroup \(H\), and let \(\lambda: G \to \text{Sym}(G/H)\) be the left-coset action, defined by \(\lambda_g(xH) : = gxH \). Then, we have that [...]
Answer
Let \(G\) be a group with subgroup \(H\), and let \(\lambda: G \to \text{Sym}(G/H)\) be the left-coset action, defined by \(\lambda_g(xH) : = gxH \). Then, we have that \( \text{Ker}(\lambda) = \bigcap_{x \in G} xHx^{-1} \)
Review
Let \(G\) be a group, and suppose \(G_1, \dots, G_n \unlhd G\) are normal subgroups such that
(1) [...]
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
(1) [...]
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
Answer
Let \(G\) be a group, and suppose \(G_1, \dots, G_n \unlhd G\) are normal subgroups such that
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
Review
Let \(G\) be a group, and suppose \(G_1, \dots, G_n \unlhd G\) are normal subgroups such that
(1) \(G_1 \dots G_n = G \)
(2) [...]
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
(1) \(G_1 \dots G_n = G \)
(2) [...]
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
Answer
Let \(G\) be a group, and suppose \(G_1, \dots, G_n \unlhd G\) are normal subgroups such that
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
Review
Let \(G\) be a group, and suppose \(G_1, \dots, G_n \unlhd G\) are normal subgroups such that
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
[...]
is an isomorphism of groups.
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
[...]
is an isomorphism of groups.
Answer
Let \(G\) be a group, and suppose \(G_1, \dots, G_n \unlhd G\) are normal subgroups such that
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
(1) \(G_1 \dots G_n = G \)
(2) \(G_k \cap (G_1 \dots G_{k-1}) = \{e\} \text{ for } k = 2, \dots, n\)
Then, the function
\(G_1 \times \dots \times G_n \to G, \quad (g_1, \dots g_n) \mapsto g_1\dots g_n \)
is an isomorphism of groups.
Review
Let \(H\) be a cyclic group of prime order \(p\), and suppose \(H\) acts on some finite set \(X\). Orbits of such an action can have size either [...]. Write \(m=\) number of orbits of size 1 and \(n=\) number of orbits of size p. Then we have
\(|X| = \) [...]
\(|X| = \) [...]
Answer
Let \(H\) be a cyclic group of prime order \(p\), and suppose \(H\) acts on some finite set \(X\). Orbits of such an action can have size either 1 or p. Write \(m=\) number of orbits of size 1 and \(n=\) number of orbits of size p. Then we have
\(|X| = \) \(m + pn \equiv m \quad (\mod p) \)
\(|X| = \) \(m + pn \equiv m \quad (\mod p) \)
Review
Let \(N \unlhd G \) be a normal subgroup, and let \( \pi: G \to G/N \) be the quotient homomorphism. If \(\phi: G \to H \) is a homomorphism such that [...] then there exists a unique homomorphism \(\psi: G/N \to H \) such that \(\psi \circ \pi = \phi \)
Answer
Let \(N \unlhd G \) be a normal subgroup, and let \( \pi: G \to G/N \) be the quotient homomorphism. If \(\phi: G \to H \) is a homomorphism such that \(\phi(N) = \{e\} \) then there exists a unique homomorphism \(\psi: G/N \to H \) such that \(\psi \circ \pi = \phi \)
Review
Let \(N \unlhd G \) be a normal subgroup, and let \( \pi: G \to G/N \) be the quotient homomorphism. If \(\phi: G \to H \) is a homomorphism such that \(\phi(N) = \{e\} \) then there exists a unique homomorphism [...]
Answer
Let \(N \unlhd G \) be a normal subgroup, and let \( \pi: G \to G/N \) be the quotient homomorphism. If \(\phi: G \to H \) is a homomorphism such that \(\phi(N) = \{e\} \) then there exists a unique homomorphism \(\psi: G/N \to H \) such that \(\psi \circ \pi = \phi \)
Review
Let \(N \unlhd G\). Then the following are equivalent:
(1) [...]
(2) \(N\) and \(G/N\) have the acc for subgroups
(1) [...]
(2) \(N\) and \(G/N\) have the acc for subgroups
Answer
Let \(N \unlhd G\). Then the following are equivalent:
(1) \(G\) has the acc for subgroups
(2) \(N\) and \(G/N\) have the acc for subgroups
(1) \(G\) has the acc for subgroups
(2) \(N\) and \(G/N\) have the acc for subgroups
Review
Let \(N \unlhd G\). Then the following are equivalent:
(1) \(G\) has the acc for subgroups
(2) [...]
(1) \(G\) has the acc for subgroups
(2) [...]
Answer
Let \(N \unlhd G\). Then the following are equivalent:
(1) \(G\) has the acc for subgroups
(2) \(N\) and \(G/N\) have the acc for subgroups
(1) \(G\) has the acc for subgroups
(2) \(N\) and \(G/N\) have the acc for subgroups
Review
Let \(p\) be a prime and \(G\) a p-group of order \(p^a, a \geq 1\). Then, [...]
Answer
Let \(p\) be a prime and \(G\) a p-group of order \(p^a, a \geq 1\). Then, \(G\) is nilpotent, and if \(a \geq 2\) it has nilpotence class \(\leq a-1\)
Review
Let G be a group acting on the nonempty set \(A\).
1. The equivalence class \(\{g\cdot a | g\in G\}\) is called the [...] of \(G\) containing \(a\)
2. The action of \(G\) is called [...] if there is only one orbit.
1. The equivalence class \(\{g\cdot a | g\in G\}\) is called the [...] of \(G\) containing \(a\)
2. The action of \(G\) is called [...] if there is only one orbit.
Answer
Let G be a group acting on the nonempty set \(A\).
1. The equivalence class \(\{g\cdot a | g\in G\}\) is called the orbit of \(G\) containing \(a\)
2. The action of \(G\) is called transitive if there is only one orbit.
1. The equivalence class \(\{g\cdot a | g\in G\}\) is called the orbit of \(G\) containing \(a\)
2. The action of \(G\) is called transitive if there is only one orbit.
Review
Name an equivalence relation of \(A\) using the action of \(G\) on a set \(A\). Name the number of elements in the equivalence class for each \(a \in A\).
Answer
Name an equivalence relation of \(A\) using the action of \(G\) on a set \(A\). Name the number of elements in the equivalence class for each \(a \in A\).
\( a \sim b \iff a = g\cdot b\)
for some \(g \in G\)
The number of elements in the equivalence class containing \(a\) is \(|G:G_a| \), the index of the stabilizer of \(a\).
\( a \sim b \iff a = g\cdot b\)
for some \(g \in G\)
The number of elements in the equivalence class containing \(a\) is \(|G:G_a| \), the index of the stabilizer of \(a\).
Review
State Cauchy's theorem.
Answer
State Cauchy's theorem.
Let \(G\) be a finite group. If a prime \(p\) divides \(|G|\), then \(G\) has an element of order \(p\)
Let \(G\) be a finite group. If a prime \(p\) divides \(|G|\), then \(G\) has an element of order \(p\)
Review
State the Class Equation for a finite group \(G\).
Answer
State the Class Equation for a finite group \(G\).
Let \(g_1, g_2, \dots g_r\) be representatives of the distinct conjugacy classes of \(G\) not contained in the center \(Z_G\). Then,
\(|G| = |Z(G)| + \sum_{i=1}^{r} |G: C_G(g_i) |\)
Let \(g_1, g_2, \dots g_r\) be representatives of the distinct conjugacy classes of \(G\) not contained in the center \(Z_G\). Then,
\(|G| = |Z(G)| + \sum_{i=1}^{r} |G: C_G(g_i) |\)
Review
State the Orbit/Stabilizer Theorem
Answer
State the Orbit/Stabilizer Theorem
Consider an action \(G\) on \(X\) and an element \(x \in X\). Then there is a bijection
\(G/G_x \to Gx, \quad gG_x \mapsto g \cdot x \)
between the orbit containing \(x\) and the set of left cosets and its stablizier. Thus, for an orbit \(\mathcal{O} \) we have \( |\mathcal{O}| = |G:G_x| \) for any \(x \in \mathcal{O} \)
Consider an action \(G\) on \(X\) and an element \(x \in X\). Then there is a bijection
\(G/G_x \to Gx, \quad gG_x \mapsto g \cdot x \)
between the orbit containing \(x\) and the set of left cosets and its stablizier. Thus, for an orbit \(\mathcal{O} \) we have \( |\mathcal{O}| = |G:G_x| \) for any \(x \in \mathcal{O} \)
Review
Suppose \(|G| = pq\) for primes \(p < q\). Let \(P \in Syl_p(G), Q \in Syl_q(G) \). Then [...]
Answer
Suppose \(|G| = pq\) for primes \(p < q\). Let \(P \in Syl_p(G), Q \in Syl_q(G) \). Then \(Q\) is normal in \(G\) and if \(P\) is also normal in \(G\), then \(G\) is cyclic
Review
Sylow's Theorem
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) [...]
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) [...]
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Answer
Sylow's Theorem
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Review
Sylow's Theorem
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that [...] In particular, any two Sylow p-subgroups of \(G\) are [...].
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that [...] In particular, any two Sylow p-subgroups of \(G\) are [...].
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Answer
Sylow's Theorem
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Review
Sylow's Theorem
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form [...], i.e., [...]
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form [...], i.e., [...]
Answer
Sylow's Theorem
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Let \(G\) be a group of order \(p^{\alpha} m\) where \(p\) is a prime not dividing \(m\).
1. Sylow p-subgroups of \(G\) exist
2. If \(P\) is a Sylow p-subgroup of \(G\) and \(Q\) is any p-subgroup of \(G\), then there exists \(g \in G\) such that \( Q \leq gPg^{-1} \) In particular, any two Sylow p-subgroups of \(G\) are conjugate in \(G\) .
3. The number of Sylow p-subgroups of \(G\) is of the form \(1+kp \) , i.e., \( n_p \equiv 1 (\mod p) \)
Review
The [...] of the action is the set of elements of \(G\) that act [...] on every element of \(A\): \(\{g \in G | g \cdot a = a, \quad a \in A\}\)
Answer
The kernel of the action is the set of elements of \(G\) that act trivially on every element of \(A\): \(\{g \in G | g \cdot a = a, \quad a \in A\}\)
Review
The center of a group \(G\) is
Answer
The center of a group \(G\) is
\(Z(G)=\{g \in G | gx = xg, \quad x \in G\} \)
\(Z(G)=\{g \in G | gx = xg, \quad x \in G\} \)
Review
The centralizer of a group \(G\) and a nonempty subset \(A\subseteq G\) is
Answer
The centralizer of a group \(G\) and a nonempty subset \(A\subseteq G\) is
\(C_G(A) = \{g \in G |gag^{-1} = a,\quad \forall a \in A \}\)
\(C_G(A) = \{g \in G |gag^{-1} = a,\quad \forall a \in A \}\)
Review
The normalizer of \(A\) in \(G\) is
Answer
The normalizer of \(A\) in \(G\) is
\(N_G(A) = \{ g\in G| gAg^{-1} = A\} \)
\(N_G(A) = \{ g\in G| gAg^{-1} = A\} \)
Review
The number of conjugates of a subset \(S\) in a group \(G\) is the [...]
Answer
The number of conjugates of a subset \(S\) in a group \(G\) is the index of the normalizer of \(S\), \(|G: N_G(S)|\)
Review
The number of conjugates of an element \(s\) of \(G\) is the [...]
Answer
The number of conjugates of an element \(s\) of \(G\) is the index of the centralizer of \(s\), \(|G : C_G(s)| \)
Review
The orbits of \(G\) acting on itself by conjugation are called the [...] of \(G\).
Answer
The orbits of \(G\) acting on itself by conjugation are called the conjugacy classes of \(G\).
Review
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. [...]
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. [...]
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Answer
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Review
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. [...]
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. [...]
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Answer
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Review
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. [...]
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. [...]
4. \(AB/B \cong A/A\cap B \)
Answer
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Review
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. [...]
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. [...]
Answer
The Second (Diamond) Isomorphism Theorem
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Let \(G\) be a group, let \(A, B\) be subgroups of \(G\) and assume \(A \leq N_G(B)\). Then
1. \(AB \leq G\)
2. \(B \unlhd AB\)
3. \(A \cap B \unlhd A \)
4. \(AB/B \cong A/A\cap B \)
Review
The Third Isomorphism Theorem
Answer
The Third Isomorphism Theorem
Let \(G\) be a group and let \(H\) and \(K\) be normal subgroups of \(G\) with \(H \leq K \). Then, \(K / H \unlhd G/H\) and
\((G/H)/(K / H) \cong G/K\)
Let \(G\) be a group and let \(H\) and \(K\) be normal subgroups of \(G\) with \(H \leq K \). Then, \(K / H \unlhd G/H\) and
\((G/H)/(K / H) \cong G/K\)
Review
The upper central series of \(G\) is constructed as follows:
- \(Z_0(G) = \{e\},Z_1(G) = Z(G) \)
- For any \(k \geq 1\) \(Z_{k + 1}(G) \) is the [...]
Answer
The upper central series of \(G\) is constructed as follows:
- \(Z_0(G) = \{e\},Z_1(G) = Z(G) \)
- For any \(k \geq 1\) \(Z_{k + 1}(G) \) is the preimage under the quotient map \(\pi : G \to G/Z_k(G) \) of \(Z (G/Z_k(G) ) \).
Review
The upper central series of \(G\) is constructed as follows:
- [...]
- For any \(k \geq 1\) \(Z_{k + 1}(G) \) is the preimage under the quotient map \(\pi : G \to G/Z_k(G) \) of \(Z (G/Z_k(G) ) \).
Answer
The upper central series of \(G\) is constructed as follows:
- \(Z_0(G) = \{e\},Z_1(G) = Z(G) \)
- For any \(k \geq 1\) \(Z_{k + 1}(G) \) is the preimage under the quotient map \(\pi : G \to G/Z_k(G) \) of \(Z (G/Z_k(G) ) \).
Review
Thus [...] of a group \(G\) on a set \(A\) and the [...] from \(G\) into the symmetric group \(S_A\) are in bijective correspondence.
Answer
Thus actions of a group \(G\) on a set \(A\) and the homomorphisms from \(G\) into the symmetric group \(S_A\) are in bijective correspondence.
Review
Two elements of \(S_n\) are conjugate in \(S_n\) if and only if they have the same [...]
Answer
Two elements of \(S_n\) are conjugate in \(S_n\) if and only if they have the same cycle type
Review
Two group elements induce the same permutation on \(A\) if and only if they are in the same [...]. In particular, an action of \(G\) on \(A\) may also be viewed as a [...] of the quotient group \(G/\text{ker}\varphi\) on \(A\)
Answer
Two group elements induce the same permutation on \(A\) if and only if they are in the same coset of the kernel. In particular, an action of \(G\) on \(A\) may also be viewed as a faithful action of the quotient group \(G/\text{ker}\varphi\) on \(A\)
Review
We say that \(G\) is an extension of \(K\) by \(H\) if [...] and isomorphisms
\(H \cong H', \quad K \cong G/H' \)
\(H \cong H', \quad K \cong G/H' \)
Answer
We say that \(G\) is an extension of \(K\) by \(H\) if there exists a normal subgroup \(H' \unlhd G\) and isomorphisms
\(H \cong H', \quad K \cong G/H' \)
\(H \cong H', \quad K \cong G/H' \)
Review
We say that \(G\) is an extension of \(K\) by \(H\) if there exists a normal subgroup \(H' \unlhd G\) and isomorphisms
[...]
[...]
Answer
We say that \(G\) is an extension of \(K\) by \(H\) if there exists a normal subgroup \(H' \unlhd G\) and isomorphisms
\(H \cong H', \quad K \cong G/H' \)
\(H \cong H', \quad K \cong G/H' \)
Review
What is a group action of a group \(G\) on a set \(A\)?
Answer
What is a group action of a group \(G\) on a set \(A\)?
A map from \(G \times A \) to \(A\) as \(g \cdot a\) for all \(g \in G\) and \(a \in A\) satisfying the following:
1. \(g_1 \cdot (g_2 \cdot a) = (g_1g_2)\cdot a, \quad g_1, g_2 \in G, a \in A\)
2. \(1 \cdot a = a, \quad a \in A\)
A map from \(G \times A \) to \(A\) as \(g \cdot a\) for all \(g \in G\) and \(a \in A\) satisfying the following:
1. \(g_1 \cdot (g_2 \cdot a) = (g_1g_2)\cdot a, \quad g_1, g_2 \in G, a \in A\)
2. \(1 \cdot a = a, \quad a \in A\)
Review
You can always extend \(K\) by \(H\) via the trivial extension, defined by [...]. The trivial extension is always split, by \(K' = \{e\} \times K \)
Answer
You can always extend \(K\) by \(H\) via the trivial extension, defined by \( G:= H \times K, \quad H' = H \times \{e\} \) . The trivial extension is always split, by \(K' = \{e\} \times K \)
Review
You can always extend \(K\) by \(H\) via the trivial extension, defined by \( G:= H \times K, \quad H' = H \times \{e\} \) . The trivial extension is always split, by [...]
Answer
You can always extend \(K\) by \(H\) via the trivial extension, defined by \( G:= H \times K, \quad H' = H \times \{e\} \) . The trivial extension is always split, by \(K' = \{e\} \times K \)
History 91 cards New: 0Learning: 0Review: 91Relearning: 0Unknown: 0
History
91 cards
Review 
Abolition of slavery in the British Empire (Slavery Abolition Act)
Event
Abolition of slavery in the British Empire (Slavery Abolition Act)
Event
1833
Major legal abolition across much of the British Empire (implementation phased).
Abolition of slavery in the British Empire (Slavery Abolition Act)
Event
Answer
Abolition of slavery in the British Empire (Slavery Abolition Act)
Event
1833
Major legal abolition across much of the British Empire (implementation phased).
Review 
Ada Lovelace
Person
Ada Lovelace
Person
10 December 1815
Mathematician often credited with early work on computing.
Ada Lovelace
Person
Answer
Ada Lovelace
Person
10 December 1815
Mathematician often credited with early work on computing.
Review 
Airplane (Wright Flyer)
Invention
Airplane (Wright Flyer)
Invention
1903
First sustained, controlled, powered heavier-than-air flight.
Airplane (Wright Flyer)
Invention
Answer
Airplane (Wright Flyer)
Invention
1903
First sustained, controlled, powered heavier-than-air flight.
Review 
Albert Einstein
Person
Albert Einstein
Person
14 March 1879
Developed relativity; major influence on modern physics.
Albert Einstein
Person
Answer
Albert Einstein
Person
14 March 1879
Developed relativity; major influence on modern physics.
Review 
Alexander the Great
Person
Alexander the Great
Person
356 BCE
King of Macedon who created a vast empire across the Eastern Mediterranean and Asia.
Alexander the Great
Person
Answer
Alexander the Great
Person
356 BCE
King of Macedon who created a vast empire across the Eastern Mediterranean and Asia.
Review 
American Civil War
War
American Civil War
War
1861–1865
Participants: Union (United States) vs Confederate States of America.
American Civil War
War
Answer
American Civil War
War
1861–1865
Participants: Union (United States) vs Confederate States of America.
Review 
American Revolutionary War
War
American Revolutionary War
War
1775–1783
Participants: Thirteen Colonies (United States) & allies vs Great Britain.
American Revolutionary War
War
Answer
American Revolutionary War
War
1775–1783
Participants: Thirteen Colonies (United States) & allies vs Great Britain.
Review 
Apollo 11 Moon landing
Event
Apollo 11 Moon landing
Event
20 July 1969
First humans land on the Moon; Neil Armstrong and Buzz Aldrin walk on the lunar surface.
Apollo 11 Moon landing
Event
Answer
Apollo 11 Moon landing
Event
20 July 1969
First humans land on the Moon; Neil Armstrong and Buzz Aldrin walk on the lunar surface.
Review 
ARPANET / early Internet
Invention
ARPANET / early Internet
Invention
1969
ARPANET’s first message is a milestone in the development of the Internet.
ARPANET / early Internet
Invention
Answer
ARPANET / early Internet
Invention
1969
ARPANET’s first message is a milestone in the development of the Internet.
Review 
Automobile (Benz Patent-Motorwagen)
Invention
Automobile (Benz Patent-Motorwagen)
Invention
1886
Often cited as the first practical modern automobile powered by an internal combustion engine.
Automobile (Benz Patent-Motorwagen)
Invention
Answer
Automobile (Benz Patent-Motorwagen)
Invention
1886
Often cited as the first practical modern automobile powered by an internal combustion engine.
Review 
Battle of Hastings
Event
Battle of Hastings
Event
1066
Norman conquest begins; William defeats Harold II.
Battle of Hastings
Event
Answer
Battle of Hastings
Event
1066
Norman conquest begins; William defeats Harold II.
Review 
Birth of the Roman Empire (Augustus becomes first emperor)
Event
Birth of the Roman Empire (Augustus becomes first emperor)
Event
27 BCE
Octavian is granted the title Augustus; end of Roman Republic.
Birth of the Roman Empire (Augustus becomes first emperor)
Event
Answer
Birth of the Roman Empire (Augustus becomes first emperor)
Event
27 BCE
Octavian is granted the title Augustus; end of Roman Republic.
Review 
Black Death in Europe (peak)
Event
Black Death in Europe (peak)
Event
1347–1351
Pandemic that killed a large share of Europe’s population.
Black Death in Europe (peak)
Event
Answer
Black Death in Europe (peak)
Event
1347–1351
Pandemic that killed a large share of Europe’s population.
Review 
Caesar’s Civil War
War
Caesar’s Civil War
War
49–45 BCE
Participants: Julius Caesar and his supporters vs Pompey and the Roman Senate faction.
Caesar’s Civil War
War
Answer
Caesar’s Civil War
War
49–45 BCE
Participants: Julius Caesar and his supporters vs Pompey and the Roman Senate faction.
Review 
Charlemagne
Person
Charlemagne
Person
2 April 742
King of the Franks and Emperor; shaped medieval Europe.
Charlemagne
Person
Answer
Charlemagne
Person
2 April 742
King of the Franks and Emperor; shaped medieval Europe.
Review 
Charles Darwin
Person
Charles Darwin
Person
12 February 1809
Developed theory of evolution by natural selection.
Charles Darwin
Person
Answer
Charles Darwin
Person
12 February 1809
Developed theory of evolution by natural selection.
Review 
Cleopatra VII
Person
Cleopatra VII
Person
69 BCE
Last active ruler of the Ptolemaic Kingdom of Egypt.
Cleopatra VII
Person
Answer
Cleopatra VII
Person
69 BCE
Last active ruler of the Ptolemaic Kingdom of Egypt.
Review 
Code of Hammurabi compiled
Event
Code of Hammurabi compiled
Event
c. 1754 BCE
One of the best-preserved ancient law codes.
Code of Hammurabi compiled
Event
Answer
Code of Hammurabi compiled
Event
c. 1754 BCE
One of the best-preserved ancient law codes.
Review 
Columbus reaches the Americas (first voyage)
Event
Columbus reaches the Americas (first voyage)
Event
1492
European arrival in the Americas triggers massive global exchange and colonization.
Columbus reaches the Americas (first voyage)
Event
Answer
Columbus reaches the Americas (first voyage)
Event
1492
European arrival in the Americas triggers massive global exchange and colonization.
Review 
Confucius
Person
Confucius
Person
551 BCE
Chinese philosopher whose teachings shaped East Asian ethics and politics.
Confucius
Person
Answer
Confucius
Person
551 BCE
Chinese philosopher whose teachings shaped East Asian ethics and politics.
Review 
Cuneiform writing
Invention
Cuneiform writing
Invention
c. 3200 BCE
One of the earliest known writing systems, used in Mesopotamia.
Cuneiform writing
Invention
Answer
Cuneiform writing
Invention
c. 3200 BCE
One of the earliest known writing systems, used in Mesopotamia.
Review 
Dante Alighieri
Person
Dante Alighieri
Person
c. 1265
Italian poet of the Divine Comedy.
Dante Alighieri
Person
Answer
Dante Alighieri
Person
c. 1265
Italian poet of the Divine Comedy.
Review 
Early agriculture (domestication of plants)
Invention
Early agriculture (domestication of plants)
Invention
c. 10,000 BCE
Early evidence of agriculture in the Fertile Crescent and other regions marks the shift to settled farming societies.
Early agriculture (domestication of plants)
Invention
Answer
Early agriculture (domestication of plants)
Invention
c. 10,000 BCE
Early evidence of agriculture in the Fertile Crescent and other regions marks the shift to settled farming societies.
Review 
Early Muslim conquests
War
Early Muslim conquests
War
632–750
Participants: Rashidun/Umayyad Caliphates vs Byzantine & Sasanian and others.
Early Muslim conquests
War
Answer
Early Muslim conquests
War
632–750
Participants: Rashidun/Umayyad Caliphates vs Byzantine & Sasanian and others.
Review 
Electric telegraph (Morse system era)
Invention
Electric telegraph (Morse system era)
Invention
1837
Telegraphy enabled rapid long-distance communication via electrical signals.
Electric telegraph (Morse system era)
Invention
Answer
Electric telegraph (Morse system era)
Invention
1837
Telegraphy enabled rapid long-distance communication via electrical signals.
Review 
Emancipation Proclamation
Event
Emancipation Proclamation
Event
1863
Declared freedom for enslaved people in Confederate states in rebellion.
Emancipation Proclamation
Event
Answer
Emancipation Proclamation
Event
1863
Declared freedom for enslaved people in Confederate states in rebellion.
Review 
English Civil War
War
English Civil War
War
1642–1651
Participants: Parliamentarians vs Royalists.
English Civil War
War
Answer
English Civil War
War
1642–1651
Participants: Parliamentarians vs Royalists.
Review 
Fall of Constantinople (Ottoman–Byzantine war)
War
Fall of Constantinople (Ottoman–Byzantine war)
War
1453
Participants: Ottoman Empire vs Byzantine Empire.
Fall of Constantinople (Ottoman–Byzantine war)
War
Answer
Fall of Constantinople (Ottoman–Byzantine war)
War
1453
Participants: Ottoman Empire vs Byzantine Empire.
Review 
Fall of Constantinople
Event
Fall of Constantinople
Event
1453
Ottomans capture Constantinople; often seen as end of Byzantine Empire.
Fall of Constantinople
Event
Answer
Fall of Constantinople
Event
1453
Ottomans capture Constantinople; often seen as end of Byzantine Empire.
Review 
Fall of the Berlin Wall
Event
Fall of the Berlin Wall
Event
9 November 1989
Symbolic end of Cold War division in Europe; leads to German reunification.
Fall of the Berlin Wall
Event
Answer
Fall of the Berlin Wall
Event
9 November 1989
Symbolic end of Cold War division in Europe; leads to German reunification.
Review 
Fall of the Western Roman Empire
Event
Fall of the Western Roman Empire
Event
476
Deposition of Romulus Augustulus often marks the end of the Western Roman Empire.
Fall of the Western Roman Empire
Event
Answer
Fall of the Western Roman Empire
Event
476
Deposition of Romulus Augustulus often marks the end of the Western Roman Empire.
Review 
First cities in Mesopotamia (Uruk period)
Event
First cities in Mesopotamia (Uruk period)
Event
c. 4000–3100 BCE
Urbanization accelerates in Mesopotamia; Uruk becomes a major early city.
First cities in Mesopotamia (Uruk period)
Event
Answer
First cities in Mesopotamia (Uruk period)
Event
c. 4000–3100 BCE
Urbanization accelerates in Mesopotamia; Uruk becomes a major early city.
Review 
First Crusade
War
First Crusade
War
1096–1099
Participants: Western European crusaders vs Seljuk Turks and other Muslim powers; culminated in capture of Jerusalem.
First Crusade
War
Answer
First Crusade
War
1096–1099
Participants: Western European crusaders vs Seljuk Turks and other Muslim powers; culminated in capture of Jerusalem.
Review 
First modern Olympic Games
Event
First modern Olympic Games
Event
1896
Revival of the Olympics in Athens.
First modern Olympic Games
Event
Answer
First modern Olympic Games
Event
1896
Revival of the Olympics in Athens.
Review 
Founding of Rome (traditional date)
Event
Founding of Rome (traditional date)
Event
753 BCE
Traditional date for Rome’s founding (historic details debated).
Founding of Rome (traditional date)
Event
Answer
Founding of Rome (traditional date)
Event
753 BCE
Traditional date for Rome’s founding (historic details debated).
Review 
French Revolution begins
Event
French Revolution begins
Event
1789
Political and social revolution that reshaped France and Europe.
French Revolution begins
Event
Answer
French Revolution begins
Event
1789
Political and social revolution that reshaped France and Europe.
Review 
Genghis Khan
Person
Genghis Khan
Person
c. 1162
Founder of the Mongol Empire (birth year approximate).
Genghis Khan
Person
Answer
Genghis Khan
Person
c. 1162
Founder of the Mongol Empire (birth year approximate).
Review 
George Washington
Person
George Washington
Person
22 February 1732
First U.S. president.
George Washington
Person
Answer
George Washington
Person
22 February 1732
First U.S. president.
Review 
Göbekli Tepe (early monumental architecture)
Event
Göbekli Tepe (early monumental architecture)
Event
c. 9600 BCE
One of the earliest known large ritual/monumental sites (approximate dating).
Göbekli Tepe (early monumental architecture)
Event
Answer
Göbekli Tepe (early monumental architecture)
Event
c. 9600 BCE
One of the earliest known large ritual/monumental sites (approximate dating).
Review 
GPS becomes fully operational
Invention
GPS becomes fully operational
Invention
1995
Global Positioning System provides precise positioning worldwide.
GPS becomes fully operational
Invention
Answer
GPS becomes fully operational
Invention
1995
Global Positioning System provides precise positioning worldwide.
Review 
Great Pyramid of Giza completed
Event
Great Pyramid of Giza completed
Event
c. 2560 BCE
Completion of Khufu’s Great Pyramid, a landmark of ancient engineering (date approximate).
Great Pyramid of Giza completed
Event
Answer
Great Pyramid of Giza completed
Event
c. 2560 BCE
Completion of Khufu’s Great Pyramid, a landmark of ancient engineering (date approximate).
Review 
Greco-Persian Wars
War
Greco-Persian Wars
War
499–449 BCE
Participants: Greek city-states (notably Athens & Sparta) vs the Achaemenid Persian Empire.
Greco-Persian Wars
War
Answer
Greco-Persian Wars
War
499–449 BCE
Participants: Greek city-states (notably Athens & Sparta) vs the Achaemenid Persian Empire.
Review 
Gunpowder
Invention
Gunpowder
Invention
9th century CE
Invented in China, gunpowder led to firearms and artillery.
Gunpowder
Invention
Answer
Gunpowder
Invention
9th century CE
Invented in China, gunpowder led to firearms and artillery.
Review 
Hijra (Muhammad's migration to Medina)
Event
Hijra (Muhammad's migration to Medina)
Event
622
Marks the start of the Islamic calendar.
Hijra (Muhammad's migration to Medina)
Event
Answer
Hijra (Muhammad's migration to Medina)
Event
622
Marks the start of the Islamic calendar.
Review 
Hundred Years' War
War
Hundred Years' War
War
1337–1453
Participants: Kingdom of England vs Kingdom of France (with allies).
Hundred Years' War
War
Answer
Hundred Years' War
War
1337–1453
Participants: Kingdom of England vs Kingdom of France (with allies).
Review 
Incandescent light bulb (practical)
Invention
Incandescent light bulb (practical)
Invention
1879
Practical electric lighting enabled widespread electrification of homes and cities.
Incandescent light bulb (practical)
Invention
Answer
Incandescent light bulb (practical)
Invention
1879
Practical electric lighting enabled widespread electrification of homes and cities.
Review 
Iron smelting (widespread)
Invention
Iron smelting (widespread)
Invention
c. 1200 BCE
Ironworking spread widely in the early Iron Age, transforming tools and warfare.
Iron smelting (widespread)
Invention
Answer
Iron smelting (widespread)
Invention
c. 1200 BCE
Ironworking spread widely in the early Iron Age, transforming tools and warfare.
Review 
Isaac Newton
Person
Isaac Newton
Person
4 January 1643
Physicist and mathematician; laws of motion and gravitation.
Isaac Newton
Person
Answer
Isaac Newton
Person
4 January 1643
Physicist and mathematician; laws of motion and gravitation.
Review 
Julius Caesar
Person
Julius Caesar
Person
12 July 100 BCE
Roman general and statesman; pivotal in the transition from Republic to Empire.
Julius Caesar
Person
Answer
Julius Caesar
Person
12 July 100 BCE
Roman general and statesman; pivotal in the transition from Republic to Empire.
Review 
Korean War
War
Korean War
War
1950–1953
Participants: North Korea & China (and allies) vs South Korea, United Nations Command led by the U.S.
Korean War
War
Answer
Korean War
War
1950–1953
Participants: North Korea & China (and allies) vs South Korea, United Nations Command led by the U.S.
Review 
Lascaux cave paintings
Event
Lascaux cave paintings
Event
c. 17,000 BCE
Famous Paleolithic cave paintings in what is now France (dates approximate).
Lascaux cave paintings
Event
Answer
Lascaux cave paintings
Event
c. 17,000 BCE
Famous Paleolithic cave paintings in what is now France (dates approximate).
Review 
Leonardo da Vinci
Person
Leonardo da Vinci
Person
15 April 1452
Renaissance polymath (artist, engineer, scientist).
Leonardo da Vinci
Person
Answer
Leonardo da Vinci
Person
15 April 1452
Renaissance polymath (artist, engineer, scientist).
Review 
Magna Carta sealed
Event
Magna Carta sealed
Event
1215
A foundational document limiting royal power in England.
Magna Carta sealed
Event
Answer
Magna Carta sealed
Event
1215
A foundational document limiting royal power in England.
Review 
Magnetic compass
Invention
Magnetic compass
Invention
c. 206 BCE
The compass enabled reliable navigation and later transformed maritime travel.
Magnetic compass
Invention
Answer
Magnetic compass
Invention
c. 206 BCE
The compass enabled reliable navigation and later transformed maritime travel.
Review 
Mahatma Gandhi
Person
Mahatma Gandhi
Person
2 October 1869
Leader of Indian independence movement.
Mahatma Gandhi
Person
Answer
Mahatma Gandhi
Person
2 October 1869
Leader of Indian independence movement.
Review 
Malala Yousafzai
Person
Malala Yousafzai
Person
12 July 1997
Pakistani activist for girls' education; Nobel laureate.
Malala Yousafzai
Person
Answer
Malala Yousafzai
Person
12 July 1997
Pakistani activist for girls' education; Nobel laureate.
Review 
Marie Curie
Person
Marie Curie
Person
7 November 1867
Pioneer in radioactivity; Nobel laureate.
Marie Curie
Person
Answer
Marie Curie
Person
7 November 1867
Pioneer in radioactivity; Nobel laureate.
Review 
Martin Luther King Jr.
Person
Martin Luther King Jr.
Person
15 January 1929
U.S. civil rights leader.
Martin Luther King Jr.
Person
Answer
Martin Luther King Jr.
Person
15 January 1929
U.S. civil rights leader.
Review 
Martin Luther posts the Ninety-five Theses
Event
Martin Luther posts the Ninety-five Theses
Event
1517
A key symbolic start of the Protestant Reformation.
Martin Luther posts the Ninety-five Theses
Event
Answer
Martin Luther posts the Ninety-five Theses
Event
1517
A key symbolic start of the Protestant Reformation.
Review 
Martin Luther
Person
Martin Luther
Person
10 November 1483
Key figure in the Protestant Reformation.
Martin Luther
Person
Answer
Martin Luther
Person
10 November 1483
Key figure in the Protestant Reformation.
Review 
Mechanical clock
Invention
Mechanical clock
Invention
c. 1300
Mechanical clocks enabled more precise timekeeping in Europe.
Mechanical clock
Invention
Answer
Mechanical clock
Invention
c. 1300
Mechanical clocks enabled more precise timekeeping in Europe.
Review 
Microprocessor (Intel 4004)
Invention
Microprocessor (Intel 4004)
Invention
1971
A CPU on a single chip, accelerating the personal computing revolution.
Microprocessor (Intel 4004)
Invention
Answer
Microprocessor (Intel 4004)
Invention
1971
A CPU on a single chip, accelerating the personal computing revolution.
Review 
Mongol conquests (Genghis Khan era begins)
War
Mongol conquests (Genghis Khan era begins)
War
1206–1279
Participants: Mongol Empire vs many states across Eurasia (Jin, Khwarazmian, Abbasid, etc.).
Mongol conquests (Genghis Khan era begins)
War
Answer
Mongol conquests (Genghis Khan era begins)
War
1206–1279
Participants: Mongol Empire vs many states across Eurasia (Jin, Khwarazmian, Abbasid, etc.).
Review 
Movable-type printing (China)
Invention
Movable-type printing (China)
Invention
c. 1040
Movable type allowed reusable characters for printing texts.
Movable-type printing (China)
Invention
Answer
Movable-type printing (China)
Invention
c. 1040
Movable type allowed reusable characters for printing texts.
Review 
Muhammad
Person
Muhammad
Person
c. 570 CE
Prophet and founder of Islam (approximate birth year).
Muhammad
Person
Answer
Muhammad
Person
c. 570 CE
Prophet and founder of Islam (approximate birth year).
Review 
Napoleon Bonaparte
Person
Napoleon Bonaparte
Person
15 August 1769
French military and political leader.
Napoleon Bonaparte
Person
Answer
Napoleon Bonaparte
Person
15 August 1769
French military and political leader.
Review 
Napoleonic Wars
War
Napoleonic Wars
War
1803–1815
Participants: First French Empire vs shifting coalitions of European powers.
Napoleonic Wars
War
Answer
Napoleonic Wars
War
1803–1815
Participants: First French Empire vs shifting coalitions of European powers.
Review 
Nelson Mandela
Person
Nelson Mandela
Person
18 July 1918
Anti-apartheid leader; President of South Africa.
Nelson Mandela
Person
Answer
Nelson Mandela
Person
18 July 1918
Anti-apartheid leader; President of South Africa.
Review 
Paper (early in China)
Invention
Paper (early in China)
Invention
2nd century BCE
Early paper artifacts appear in China before later standardization of papermaking.
Paper (early in China)
Invention
Answer
Paper (early in China)
Invention
2nd century BCE
Early paper artifacts appear in China before later standardization of papermaking.
Review 
Penicillin discovered
Invention
Penicillin discovered
Invention
1928
Fleming’s discovery led to antibiotics that saved millions of lives.
Penicillin discovered
Invention
Answer
Penicillin discovered
Invention
1928
Fleming’s discovery led to antibiotics that saved millions of lives.
Review 
Printing press (Gutenberg)
Invention
Printing press (Gutenberg)
Invention
c. 1450
Mass printing accelerated the spread of literacy and ideas in Europe.
Printing press (Gutenberg)
Invention
Answer
Printing press (Gutenberg)
Invention
c. 1450
Mass printing accelerated the spread of literacy and ideas in Europe.
Review 
Qin unifies China
Event
Qin unifies China
Event
221 BCE
Qin Shi Huang completes the unification of China, founding the Qin dynasty.
Qin unifies China
Event
Answer
Qin unifies China
Event
221 BCE
Qin Shi Huang completes the unification of China, founding the Qin dynasty.
Review 
Russo-Japanese War
War
Russo-Japanese War
War
1904–1905
Participants: Russian Empire vs Empire of Japan.
Russo-Japanese War
War
Answer
Russo-Japanese War
War
1904–1905
Participants: Russian Empire vs Empire of Japan.
Review 
Seven Years' War
War
Seven Years' War
War
1756–1763
Participants: Great Britain & allies vs France & allies (global conflict involving Prussia, Austria, Russia, etc.).
Seven Years' War
War
Answer
Seven Years' War
War
1756–1763
Participants: Great Britain & allies vs France & allies (global conflict involving Prussia, Austria, Russia, etc.).
Review 
Siddhartha Gautama (Buddha)
Person
Siddhartha Gautama (Buddha)
Person
c. 563 BCE (traditional)
Founder of Buddhism (dates debated; traditional dates shown).
Siddhartha Gautama (Buddha)
Person
Answer
Siddhartha Gautama (Buddha)
Person
c. 563 BCE (traditional)
Founder of Buddhism (dates debated; traditional dates shown).
Review 
Smallpox vaccination (Jenner)
Invention
Smallpox vaccination (Jenner)
Invention
1796
Jenner’s method pioneered vaccination and modern immunology.
Smallpox vaccination (Jenner)
Invention
Answer
Smallpox vaccination (Jenner)
Invention
1796
Jenner’s method pioneered vaccination and modern immunology.
Review 
Smartphone era (iPhone)
Invention
Smartphone era (iPhone)
Invention
2007
Popularized multi-touch smartphones and modern app ecosystems.
Smartphone era (iPhone)
Invention
Answer
Smartphone era (iPhone)
Invention
2007
Popularized multi-touch smartphones and modern app ecosystems.
Review 
Spinning jenny
Invention
Spinning jenny
Invention
1764
A multi-spindle spinning frame that boosted textile production during the Industrial Revolution.
Spinning jenny
Invention
Answer
Spinning jenny
Invention
1764
A multi-spindle spinning frame that boosted textile production during the Industrial Revolution.
Review 
Steam engine (Newcomen)
Invention
Steam engine (Newcomen)
Invention
1712
Early practical steam engines powered pumping and, later, industrial machinery.
Steam engine (Newcomen)
Invention
Answer
Steam engine (Newcomen)
Invention
1712
Early practical steam engines powered pumping and, later, industrial machinery.
Review 
Telephone
Invention
Telephone
Invention
1876
Voice transmission over electrical networks transformed communication.
Telephone
Invention
Answer
Telephone
Invention
1876
Voice transmission over electrical networks transformed communication.
Review 
Telescope
Invention
Telescope
Invention
1608
Early telescopes revolutionized astronomy; Galileo soon improved and used them for observation.
Telescope
Invention
Answer
Telescope
Invention
1608
Early telescopes revolutionized astronomy; Galileo soon improved and used them for observation.
Review 
Thirty Years' War
War
Thirty Years' War
War
1618–1648
Participants: many European powers; key participants include the Holy Roman Empire/Habsburgs vs various Protestant states, with Sweden and France involved.
Thirty Years' War
War
Answer
Thirty Years' War
War
1618–1648
Participants: many European powers; key participants include the Holy Roman Empire/Habsburgs vs various Protestant states, with Sweden and France involved.
Review 
Transistor
Invention
Transistor
Invention
1947
The transistor became a foundational component of modern electronics.
Transistor
Invention
Answer
Transistor
Invention
1947
The transistor became a foundational component of modern electronics.
Review 
United Nations founded
Event
United Nations founded
Event
24 October 1945
UN Charter enters into force; a new global intergovernmental organization forms.
United Nations founded
Event
Answer
United Nations founded
Event
24 October 1945
UN Charter enters into force; a new global intergovernmental organization forms.
Review 
Vietnam War
War
Vietnam War
War
1955–1975
Participants: North Vietnam & Viet Cong vs South Vietnam and the United States and allies.
Vietnam War
War
Answer
Vietnam War
War
1955–1975
Participants: North Vietnam & Viet Cong vs South Vietnam and the United States and allies.
Review 
Viking invasions of England (Great Heathen Army)
War
Viking invasions of England (Great Heathen Army)
War
865–878
Participants: Viking forces (Danes) vs Anglo-Saxon kingdoms.
Viking invasions of England (Great Heathen Army)
War
Answer
Viking invasions of England (Great Heathen Army)
War
865–878
Participants: Viking forces (Danes) vs Anglo-Saxon kingdoms.
Review 
Wheel
Invention
Wheel
Invention
c. 3500 BCE
The wheel enabled wheeled vehicles and new forms of transport and machinery.
Wheel
Invention
Answer
Wheel
Invention
c. 3500 BCE
The wheel enabled wheeled vehicles and new forms of transport and machinery.
Review 
William Shakespeare
Person
William Shakespeare
Person
26 April 1564
English playwright and poet.
William Shakespeare
Person
Answer
William Shakespeare
Person
26 April 1564
English playwright and poet.
Review 
William the Conqueror
Person
William the Conqueror
Person
c. 1028
Duke of Normandy who became King of England in 1066.
William the Conqueror
Person
Answer
William the Conqueror
Person
c. 1028
Duke of Normandy who became King of England in 1066.
Review 
World War II
War
World War II
War
1939–1945
Participants: Axis powers vs Allies.
World War II
War
Answer
World War II
War
1939–1945
Participants: Axis powers vs Allies.
Review 
World War I
War
World War I
War
1914–1918
Participants: Central Powers vs Allied Powers.
World War I
War
Answer
World War I
War
1914–1918
Participants: Central Powers vs Allied Powers.
Plants 90 cards New: 32Learning: 0Review: 58Relearning: 0Unknown: 0
Plants
90 cards
Review 
Giant sequoia
Answer
Giant sequoia
Review 
Coast redwood
Answer
Coast redwood
Review 
Oak
Answer
Oak
Review 
Maple
Answer
Maple
Review 
Cedar
Answer
Cedar
Review 
Birch
Answer
Birch
Review 
Willow
Answer
Willow
Review 
Baobab
Answer
Baobab
Review 
Banyan
Answer
Banyan
Review 
Olive tree
Answer
Olive tree
Review 
Ginkgo biloba
Answer
Ginkgo biloba
Review 
Eucalyptus
Answer
Eucalyptus
Review .JPG)
Mangrove
Answer
Mangrove
Review 
Spruce
Answer
Spruce
Review .JPG)
Fir
Answer
Fir
Review 
Chestnut
Answer
Chestnut
Review 
Fig tree
Answer
Fig tree
Review 
Teak
Answer
Teak
Review .jpg)
Mahogany
Answer
Mahogany
Review 
Ash
Answer
Ash
Review 
Poplar
Answer
Poplar
Review 
Sycamore
Answer
Sycamore
Review 
Juniper
Answer
Juniper
Review 
Yew
Answer
Yew
Review 
Dogwood
Answer
Dogwood
Review 
Rose
Answer
Rose
Review 
Tulip
Answer
Tulip
Review 
Orchid
Answer
Orchid
Review 
Lotus
Answer
Lotus
Review 
Lily
Answer
Lily
Review 
Daisy
Answer
Daisy
Review 
Daffodil
Answer
Daffodil
Review 
Marigold
Answer
Marigold
Review 
Lavender
Answer
Lavender
Review 
Hibiscus
Answer
Hibiscus
Review 
Peony
Answer
Peony
Review 
Chrysanthemum
Answer
Chrysanthemum
Review 
Poppy
Answer
Poppy
Review 
Iris
Answer
Iris
Review 
Jasmine
Answer
Jasmine
Review 
Magnolia
Answer
Magnolia
Review 
Camellia
Answer
Camellia
Review 
Gardenia
Answer
Gardenia
Review .jpg)
Bluebell
Answer
Bluebell
Review .jpg)
Snapdragon
Answer
Snapdragon
Review 
Zinnia
Answer
Zinnia
Review 
Begonia
Answer
Begonia
Review 
Petunia
Answer
Petunia
Review 
Foxglove
Answer
Foxglove
Review 
Wisteria
Answer
Wisteria
Review 
Hydrangea
Answer
Hydrangea
Review 
Anemone
Answer
Anemone
Review 
Edelweiss
Answer
Edelweiss
Review 
Morning glory
Answer
Morning glory
Review 
Rice
Answer
Rice
Review _-_United_States_National_Arboretum_-_24_May_2009.jpg)
Barley
Answer
Barley
New 
Oats
Answer
Oats
New 
Rye
Answer
Rye
New 
Potato
Answer
Potato
New 
Sweet potato
Answer
Sweet potato
New 
Cassava
Answer
Cassava
New 
Sugarcane
Answer
Sugarcane
New 
Coffee plant
Answer
Coffee plant
Review 
Tea plant
Answer
Tea plant
New 
Cocoa tree
Answer
Cocoa tree
New 
Banana plant
Answer
Banana plant
New 
Coconut palm
Answer
Coconut palm
New 
Soybean
Answer
Soybean
New 
Peanut
Answer
Peanut
New 
Cotton
Answer
Cotton
New _BHL303594.jpg)
Flax
Answer
Flax
New 
Hemp
Answer
Hemp
New 
Grape vine
Answer
Grape vine
New 
Tomato plant
Answer
Tomato plant
New 
Chili pepper
Answer
Chili pepper
New 
Saguaro cactus
Answer
Saguaro cactus
New 
Prickly pear cactus
Answer
Prickly pear cactus
New 
Venus flytrap
Answer
Venus flytrap
New 
Pitcher plant
Answer
Pitcher plant
New 
Sundew
Answer
Sundew
Review 
Cycad
Answer
Cycad
New 
Fern
Answer
Fern
New 
Moss
Answer
Moss
New 
Horsetail
Answer
Horsetail
New 
Bamboo
Answer
Bamboo
New 
Kelp
Answer
Kelp
New 
Sea lettuce
Answer
Sea lettuce
New 
Aloe vera
Answer
Aloe vera
New 
Agave
Answer
Agave
New 
Rubber tree
Answer
Rubber tree
Squares 84 cards New: 49Learning: 0Review: 35Relearning: 0Unknown: 0
Squares
84 cards
Review
\(13^2\)
Answer
\(13^2\)
169
169
Review
\(14^2\)
Answer
\(14^2\)
196
196
Review
\(15^2\)
Answer
\(15^2\)
225
225
Review
\(16^2\)
Answer
\(16^2\)
256
256
Review
\(17^2\)
Answer
\(17^2\)
289
289
Review
\(18^2\)
Answer
\(18^2\)
324
324
Review
\(19^2\)
Answer
\(19^2\)
361
361
Review
\(21^2\)
Answer
\(21^2\)
441
441
Review
\(22^2\)
Answer
\(22^2\)
484
484
Review
\(23^2\)
Answer
\(23^2\)
529
529
Review
\(24^2\)
Answer
\(24^2\)
576
576
Review
\(25^2\)
Answer
\(25^2\)
625
625
Review
\(26^2\)
Answer
\(26^2\)
676
676
Review
\(27^2\)
Answer
\(27^2\)
729
729
Review
\(28^2\)
Answer
\(28^2\)
784
784
Review
\(29^2\)
Answer
\(29^2\)
841
841
Review
\(31^2\)
Answer
\(31^2\)
961
961
Review
\(32^2\)
Answer
\(32^2\)
1024
1024
Review
\(33^2\)
Answer
\(33^2\)
1089
1089
Review
\(34^2\)
Answer
\(34^2\)
1156
1156
Review
\(35^2\)
Answer
\(35^2\)
1225
1225
Review
\(36^2\)
Answer
\(36^2\)
1296
1296
Review
\(37^2\)
Answer
\(37^2\)
1369
1369
Review
\(38^2\)
Answer
\(38^2\)
1444
1444
Review
\(39^2\)
Answer
\(39^2\)
1521
1521
Review
\(41^2\)
Answer
\(41^2\)
1681
1681
Review
\(42^2\)
Answer
\(42^2\)
1764
1764
Review
\(43^2\)
Answer
\(43^2\)
1849
1849
Review
\(44^2\)
Answer
\(44^2\)
1936
1936
New
\(45^2\)
Answer
\(45^2\)
2025
2025
New
\(46^2\)
Answer
\(46^2\)
2116
2116
New
\(47^2\)
Answer
\(47^2\)
2209
2209
New
\(48^2\)
Answer
\(48^2\)
2304
2304
New
\(49^2\)
Answer
\(49^2\)
2401
2401
New
\(50^2\)
Answer
\(50^2\)
2500
2500
Review
\(51^2\)
Answer
\(51^2\)
2601
2601
New
\(52^2\)
Answer
\(52^2\)
2704
2704
New
\(53^2\)
Answer
\(53^2\)
2809
2809
New
\(54^2\)
Answer
\(54^2\)
2916
2916
New
\(55^2\)
Answer
\(55^2\)
3025
3025
New
\(56^2\)
Answer
\(56^2\)
3136
3136
New
\(57^2\)
Answer
\(57^2\)
3249
3249
New
\(58^2\)
Answer
\(58^2\)
3364
3364
New
\(59^2\)
Answer
\(59^2\)
3481
3481
New
\(60^2\)
Answer
\(60^2\)
3600
3600
Review
\(61^2\)
Answer
\(61^2\)
3721
3721
New
\(62^2\)
Answer
\(62^2\)
3844
3844
New
\(63^2\)
Answer
\(63^2\)
3969
3969
New
\(64^2\)
Answer
\(64^2\)
4096
4096
Review
\(65^2\)
Answer
\(65^2\)
4225
4225
New
\(66^2\)
Answer
\(66^2\)
4356
4356
New
\(67^2\)
Answer
\(67^2\)
4489
4489
New
\(68^2\)
Answer
\(68^2\)
4624
4624
Review
\(69^2\)
Answer
\(69^2\)
4761
4761
New
\(70^2\)
Answer
\(70^2\)
4900
4900
New
\(71^2\)
Answer
\(71^2\)
5041
5041
New
\(72^2\)
Answer
\(72^2\)
5184
5184
New
\(73^2\)
Answer
\(73^2\)
5329
5329
New
\(74^2\)
Answer
\(74^2\)
5476
5476
New
\(75^2\)
Answer
\(75^2\)
5625
5625
New
\(76^2\)
Answer
\(76^2\)
5776
5776
New
\(77^2\)
Answer
\(77^2\)
5929
5929
New
\(78^2\)
Answer
\(78^2\)
6084
6084
New
\(79^2\)
Answer
\(79^2\)
6241
6241
New
\(80^2\)
Answer
\(80^2\)
6400
6400
New
\(81^2\)
Answer
\(81^2\)
6561
6561
New
\(82^2\)
Answer
\(82^2\)
6724
6724
New
\(83^2\)
Answer
\(83^2\)
6889
6889
New
\(84^2\)
Answer
\(84^2\)
7056
7056
New
\(85^2\)
Answer
\(85^2\)
7225
7225
New
\(86^2\)
Answer
\(86^2\)
7396
7396
New
\(87^2\)
Answer
\(87^2\)
7569
7569
New
\(88^2\)
Answer
\(88^2\)
7744
7744
New
\(89^2\)
Answer
\(89^2\)
7921
7921
New
\(90^2\)
Answer
\(90^2\)
8100
8100
New
\(91^2\)
Answer
\(91^2\)
8281
8281
New
\(92^2\)
Answer
\(92^2\)
8464
8464
New
\(93^2\)
Answer
\(93^2\)
8649
8649
Review
\(94^2\)
Answer
\(94^2\)
8836
8836
New
\(95^2\)
Answer
\(95^2\)
9025
9025
Review
\(96^2\)
Answer
\(96^2\)
9216
9216
New
\(97^2\)
Answer
\(97^2\)
9409
9409
New
\(98^2\)
Answer
\(98^2\)
9604
9604
New
\(99^2\)
Answer
\(99^2\)
9801
9801
Ultimate Geography 243 cards New: 185Learning: 0Review: 58Relearning: 0Unknown: 0
Ultimate Geography
243 cards
Review
?
Location
Answer
Wales
Constituent country of the United Kingdom.
Location
Review
?
Location
Answer
Georgia
Location
Review
?
Location
Answer
Germany
Location
Review
?
Location
Answer
Greece
Location
Review
?
Location
Answer
Greenland
Constituent country in the Kingdom of Denmark.
Location
Review
?
Location
Answer
Hungary
Location
Review
?
Location
Answer
Albania
Location
Review
?
Location
Answer
Andorra
Location
Review
?
Location
Answer
Austria
Location
Review
?
Location
Answer
Azerbaijan
Location
Review
?
Location
Answer
Belarus
Location
Review
?
Location
Answer
Belgium
Location
Review
?
Location
Answer
Bosnia and Herzegovina
Location
Review
?
Location
Answer
Bulgaria
Location
Review
?
Location
Answer
Croatia
Location
New
?
Location
Answer
Czech Republic
Also known as Czechia.
Location
New
?
Location
Answer
Denmark
Location
New
?
Location
Answer
Estonia
Location
New
?
Location
Answer
Faroe Islands
Constituent country in the Kingdom of Denmark.
Location
New
?
Location
Answer
Finland
Location
Review
?
Location
Answer
Iceland
Location
Review
?
Location
Answer
Ireland
Location
Review
?
Location
Answer
Latvia
Location
New
?
Location
Answer
Liechtenstein
Location
New
?
Location
Answer
Lithuania
Location
New
?
Location
Answer
Luxembourg
Location
Review
?
Location
Answer
North Macedonia
Formerly known as Macedonia.
Location
New
?
Location
Answer
Malta
Location
Review
?
Location
Answer
Moldova
Location
Review
?
Location
Answer
Monaco
Location
New
?
Location
Answer
Montenegro
Location
Review
?
Location
Answer
Netherlands
Location
Review
?
Location
Answer
Norway
Location
Review
?
Location
Answer
Poland
Location
New
?
Location
Answer
Portugal
Location
New
?
Location
Answer
Romania
Location
New
?
Location
Answer
Russia
Location
New
?
Location
Answer
San Marino
Location
New
?
Location
Answer
Serbia
Location
Review
?
Location
Answer
Slovakia
Location
Review
?
Location
Answer
Slovenia
Location
New
?
Location
Answer
Spain
Location
New
?
Location
Answer
Sweden
Location
New
?
Location
Answer
Switzerland
Location
New
?
Location
Answer
Turkey
Location
New
?
Location
Answer
Ukraine
Location
New
?
Location
Answer
Vatican City
Location
New
?
Location
Answer
Armenia
Location
New
?
Location
Answer
Kazakhstan
Location
Review
?
Location
Answer
Egypt
Location
New
?
Location
Answer
Algeria
Location
New
?
Location
Answer
Angola
Location
Review
?
Location
Answer
Benin
Location
New
?
Location
Answer
Botswana
Location
New
?
Location
Answer
Burkina Faso
Location
Review
?
Location
Answer
Cameroon
Location
New
?
Location
Answer
Burundi
Location
New
?
Location
Answer
Cape Verde
Also known as Cabo Verde.
Location
New
?
Location
Answer
São Tomé and Príncipe
Location
New
?
Location
Answer
Central African Republic
Location
New
?
Location
Answer
Chad
Location
New
?
Location
Answer
Equatorial Guinea
Location
New
?
Location
Answer
Kenya
Location
New
?
Location
Answer
Comoros
Location
Review
?
Location
Answer
Ivory Coast
Officially Côte d'Ivoire.
Location
New
?
Location
Answer
Democratic Republic of the Congo
Formerly Zaire.
Location
Review
?
Location
Answer
Djibouti
Location
New
?
Location
Answer
Guinea-Bissau
Location
New
?
Location
Answer
Eritrea
Location
New
?
Location
Answer
Ethiopia
Location
New
?
Location
Answer
Gabon
Location
New
?
Location
Answer
The Gambia
Location
New
?
Location
Answer
Lesotho
Location
New
?
Location
Answer
Liberia
Location
New
?
Location
Answer
Madagascar
Location
New
?
Location
Answer
Malawi
Location
Review
?
Location
Answer
Mali
Location
New
?
Location
Answer
Mauritania
Location
New
?
Location
Answer
Mauritius
Location
New
?
Location
Answer
Morocco
Location
New
?
Location
Answer
Mozambique
Location
New
?
Location
Answer
Namibia
Location
New
?
Location
Answer
Niger
Location
New
?
Location
Answer
Nigeria
Location
New
?
Location
Answer
Republic of the Congo
Location
New
?
Location
Answer
Rwanda
Location
Review
?
Location
Answer
Senegal
Location
New
?
Location
Answer
Seychelles
Location
New
?
Location
Answer
Sierra Leone
Location
Review
?
Location
Answer
South Africa
Location
Review
?
Location
Answer
Sudan
Location
Review
?
Location
Answer
Eswatini
Known as Swaziland until 2018.
Location
Review
?
Location
Answer
Tanzania
Location
New
?
Location
Answer
Togo
Location
New
?
Location
Answer
Tunisia
Location
New
?
Location
Answer
Uganda
Location
New
?
Location
Answer
Zambia
Location
New
?
Location
Answer
Zimbabwe
Location
New
?
Location
Answer
Canary Islands
Autonomous community of Spain.
Location
New
?
Location
Answer
Afghanistan
Location
Review
?
Location
Answer
Bahrain
Location
New
?
Location
Answer
Bangladesh
Location
New
?
Location
Answer
Bhutan
Location
New
?
Location
Answer
Brunei
Location
New
?
Location
Answer
China
Location
New
?
Location
Answer
Cambodia
Location
Review
?
Location
Answer
Indonesia
Location
New
?
Location
Answer
India
Location
New
?
Location
Answer
Hong Kong
Special Administrative Region of China.
Location
New
?
Location
Answer
Iran
Location
New
?
Location
Answer
Israel
Location
Review
?
Location
Answer
Iraq
Location
Review
?
Location
Answer
South Korea
Location
New
?
Location
Answer
North Korea
Location
New
?
Location
Answer
Jordan
Location
New
?
Location
Answer
Japan
Location
New
?
Location
Answer
Lebanon
Location
New
?
Location
Answer
Laos
Location
New
?
Location
Answer
Kyrgyzstan
Location
New
?
Location
Answer
Kuwait
Location
New
?
Location
Answer
Myanmar
Also known as Burma.
Location
New
?
Location
Answer
Mongolia
Location
New
?
Location
Answer
Maldives
Location
New
?
Location
Answer
Malaysia
Location
New
?
Location
Answer
Oman
Location
New
?
Location
Answer
Nepal
Location
Review
?
Location
Answer
Palestine
Location
New
?
Location
Answer
Pakistan
Location
Review
?
Location
Answer
Qatar
Location
New
?
Location
Answer
Saudi Arabia
Location
New
?
Location
Answer
Singapore
Location
Review
?
Location
Answer
Syria
Location
New
?
Location
Answer
Taiwan
Partially recognised state claimed by China.
Location
Review
?
Location
Answer
Sri Lanka
Location
New
?
Location
Answer
Tajikistan
Location
New
?
Location
Answer
Thailand
Location
New
?
Location
Answer
East Timor
Also known as Timor-Leste.
Location
New
?
Location
Answer
United Arab Emirates
Location
New
?
Location
Answer
Turkmenistan
Location
Review
?
Location
Answer
Yemen
Location
New
?
Location
Answer
Vietnam
Location
New
?
Location
Answer
Uzbekistan
Location
New
?
Location
Answer
Fiji
Location
New
?
Location
Answer
Papua New Guinea
Location
Review
?
Location
Answer
Australia
Location
New
?
Location
Answer
Solomon Islands
Location
New
?
Location
Answer
Argentina
Location
Review
?
Location
Answer
Bolivia
Location
New
?
Location
Answer
Brazil
Location
New
?
Location
Answer
Chile
Location
New
?
Location
Answer
Colombia
Location
New
?
Location
Answer
Ecuador
Location
New
?
Location
Answer
Guyana
Location
New
?
Location
Answer
Paraguay
Location
New
?
Location
Answer
Peru
Location
New
?
Location
Answer
Suriname
Location
New
?
Location
Answer
Uruguay
Location
New
?
Location
Answer
Venezuela
Location
New
?
Location
Answer
Cook Islands
Location
New
?
Location
Answer
Federated States of Micronesia
Location
New
?
Location
Answer
Guam
Unincorporated territory of the United States.
Location
New
?
Location
Answer
Vanuatu
Location
New
?
Location
Answer
Canada
Location
Review
?
Location
Answer
Puerto Rico
Unincorporated territory of the United States.
Location
Review
?
Location
Answer
Cuba
Location
Review
?
Location
Answer
Dominican Republic
Location
New
?
Location
Answer
Haiti
Location
New
?
Location
Answer
Jamaica
Location
New
?
Location
Answer
Trinidad and Tobago
Location
New
?
Location
Answer
Bermuda
Overseas territory of the United Kingdom.
Location
New
?
Location
Answer
Guadeloupe
Overseas department of France.
Location
New
?
Location
Answer
The Bahamas
Location
New
?
Location
Answer
Barbados
Location
New
?
Location
Answer
Belize
Location
New
?
Location
Answer
Costa Rica
Location
Review
?
Location
Answer
El Salvador
Location
New
?
Location
Answer
Guatemala
Location
New
?
Location
Answer
Honduras
Location
Review
?
Location
Answer
Nicaragua
Location
New
?
Location
Answer
Panama
Location
New
?
Location
Answer
Antigua and Barbuda
Location
New
?
Location
Answer
Dominica
Location
New
?
Location
Answer
Saint Vincent and the Grenadines
Location
New
?
Location
Answer
Somalia
Location
New
?
Location
Answer
Zanzibar
Semi-autonomous region of Tanzania.
Location
New
?
Location
Answer
Ghana
Location
Review
?
Location
Answer
Guinea
Location
Review
?
Location
Answer
New Zealand
Location
New
?
Location
Answer
French Polynesia
Overseas territory of France.
Location
New
?
Location
Answer
Philippines
Location
New
?
Location
Answer
Kosovo
Partially recognised state claimed by Serbia.
Location
New
?
Location
Answer
Libya
Location
New
?
Location
Answer
Palau
Location
New
?
Location
Answer
Saint Lucia
Location
Review
?
Location
Answer
Bali
Island of Indonesia.
Location
New
?
Location
Answer
Grenada
Location
New
?
Location
Answer
British Virgin Islands
Overseas territory of the United Kingdom.
Location
New
?
Location
Answer
Turks and Caicos Islands
Overseas territory of the United Kingdom.
Location
New
?
Location
Answer
Cayman Islands
Overseas territory of the United Kingdom.
Location
New
?
Location
Answer
Pacific Ocean
Location
New
?
Location
Answer
Atlantic Ocean
Location
New
?
Location
Answer
Indian Ocean
Location
New
?
Location
Answer
Arctic Ocean
Location
New
?
Location
Answer
Hudson Bay
Location
New
?
Location
Answer
Labrador Sea
Location
New
?
Location
Answer
White Sea
Location
New
?
Location
Answer
Denmark Strait
Location
New
?
Location
Answer
Norwegian Sea
Location
New
?
Location
Answer
Baltic Sea
Location
New
?
Location
Answer
Celtic Sea
Location
New
?
Location
Answer
English Channel
Location
New
?
Location
Answer
Adriatic Sea
Location
New
?
Location
Answer
Bay of Biscay
Location
New
?
Location
Answer
Black Sea
Location
New
?
Location
Answer
Aegean Sea
Location
New
?
Location
Answer
Balkan Peninsula
Location
New
?
Location
Answer
Caspian Sea
Location
New
?
Location
Answer
Mediterranean Sea
Location
New
?
Location
Answer
East Siberian Sea
Location
New
?
Location
Answer
Bering Strait
Location
New
?
Location
Answer
Arabian Sea
Location
New
?
Location
Answer
Red Sea
Location
New
?
Location
Answer
Dead Sea
Location
New
?
Location
Answer
Bay of Bengal
Location
New
?
Location
Answer
Sea of Japan
A naming dispute exists between the sea's bordering countries, with South Korea notably supporting the name East Sea.
Location
New
?
Location
Answer
Yellow Sea
Location
New
?
Location
Answer
Coral Sea
Location
New
?
Location
Answer
South China Sea
Location
New
?
Location
Answer
Tasman Sea
Location
New
?
Location
Answer
Gulf of Carpentaria
Location
New
?
Location
Answer
Aral Sea
Location
New
?
Location
Answer
Persian Gulf
Location
New
?
Location
Answer
Caribbean Sea
Location
New
?
Location
Answer
Gulf of California
Also known as the Sea of Cortez.
Location
New
?
Location
Answer
Polynesia
Subregion of Oceania comprising thousands of small islands in the central and southern Pacific Ocean.
Location
Review
?
Location
Answer
Melanesia
Subregion of Oceania, which includes the four countries of Vanuatu, the Solomon Islands, Fiji, and Papua New Guinea.
Location
Review
?
Location
Answer
Scandinavia
Historical and cultural region in Northern Europe, which includes the countries of Denmark, Norway and Sweden, and sometimes Finland and Iceland.
Location
New
?
Location
Answer
Sea of Galilee
Location
New
?
Location
Answer
Sumatra
Island of Indonesia.
Location
New
?
Location
Answer
Sicily
Autonomous region of Italy.
Location
New
?
Location
Answer
Mayotte
Overseas department of France.
Location
New
?
Location
Answer
Réunion
Overseas department of France.
Location
New
?
Location
Answer
Falkland Islands
Overseas territory of the United Kingdom.
Location