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Mathematical abelian group
In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces the
Klein_four-group
Topics referred to by the same term
Four group or Group of Four may refer to: Klein four-group Four note group G4 nations Lucky Four Group Clause Four Group Gang of Four (disambiguation)
Four_group
Research method developed by Richard Solomon
The Solomon four-group design is a research method developed by Richard Solomon in 1949. It is sometimes used in social science, psychology and medicine
Solomon_four-group_design
American hip hop group
The Fearless Four (also known as Fearless 4 and Fearless Four) is an American old school hip hop group from Harlem, New York. The group is best known for
The_Fearless_Four_(group)
British student politics group
Clause Four was a group in British student politics in the 1970s and 1980s, set up to oppose Militant in the National Organisation of Labour Students (NOLS)
Clause_Four_Group
In music, four note group patterns, alternately called "four-note digital patterns" or simply "four note patterns", are one of many ways to formulate
Four_note_group
Natural number
four elements; it is the Klein four-group. An alternating groups are not simple for values n {\displaystyle n} ≤ 4 {\displaystyle 4} . There are four
4
Group of symmetries of a regular polygon
mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest
Dihedral_group
Chinese Cultural Revolution faction
commanded by supporters of the radical group were placed on a heightened state of readiness. After Mao died, the four represented a quarter of the remaining
Gang_of_Four
Motor vehicle
(ALS) in their Group A ST205 Celica GT-Four rally cars, a technological breakthrough that was later adopted by other teams. The Celica GT-Four introduced
Toyota_Celica_GT-Four
Group of mountains in British Columbia
The Lucky Four Group is the name for a group of four mountains in the Cheam Range of the North Cascades of British Columbia east of the city of Chilliwack
Lucky_Four_Group
Cultural and political alliance in Europe
The Visegrád Group (also known as the Visegrád Four or the V4) is a cultural and political alliance of four Central European countries: the Czech Republic
Visegrád_Group
a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere
Point groups in four dimensions
Point_groups_in_four_dimensions
Detroit band
The Fantastic Four (also known as Sweet James and The Fantastic Four) were a Detroit based soul vocal group, formed in 1965. "Sweet" James Epps, brothers
The_Fantastic_Four_(band)
European football competition
and relegation. The first tournament was in September 2018, with the four group winners from League A qualifying for the first finals, played in Portugal
UEFA_Nations_League
American jazz band
Chuck Flores was the group's original drummer but did not record with them. The group toured Australia in 1975. 1975: The L.A. Four Scores! (Concord Jazz)
The_L.A._Four_(band)
Holding company (2007–2012)
Four Points Media Group LLC was a holding company owned by Cerberus Capital Management, established in 2007 to serve as a buyer for 7 television stations
Four_Points_Media_Group
Type of group in abstract algebra
the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the
Symmetric_group
Ancient Greek and Roman system of medicine involving four fluid types
seen it? What can we say of this fanciful classification of humors into four groups, of which two are absolutely imaginary?" The seasonal association of
Humorism
Association football tournament in Uruguay
to the Great Depression. The teams were divided into four groups, with the winner of each group progressing to the semi-finals. The first two World Cup
1930_FIFA_World_Cup
Group of even permutations of a finite set
smallest non-abelian simple group, having order 60, and thus the smallest non-solvable group. The group A4 has the Klein four-group V as a proper normal subgroup
Alternating_group
European basketball championship
The EuroLeague Final Four is the final four format championship of the European-wide top-tier level EuroLeague professional club basketball competition
EuroLeague_Final_Four
Mathematical group
Galois group of a certain type of field extension is a symmetry group characterizing how it extends the base field. Each element of the Galois group is a
Galois_group
American band
the Four Seasons. They are one of the best-selling musical groups of all time, having sold an estimated 100 million records worldwide. The Four Seasons
The_Four_Seasons_(band)
Motorsport regulation for cars
the first place. Group B could be used to homologate production sports cars which were ineligible for Group N or A due to not having four seats or not being
Group_B
Topics referred to by the same term
LA-4 or LA Four may refer to: Louisiana Highway 4, abbreviated as LA 4 Louisiana's 4th congressional district, abbreviated as LA-4 "L.A. Four", the media
LA_4
Barbershop quartet from New York (1955–1960)
group appeared on the Arthur Godfrey television programme and ..." Billboard - February 4, 1956 - Page 20 "The Four Voices, Columbia recording group,
The_Four_Voices
Former third tier of the football pyramid of professional football league in Spain
into 4 groups of 20. The top four teams from each group, 16 teams in total, qualify for play-offs to determine which four teams will replace the four teams
Segunda_División_B
Award
The Group Medal of the Four Day Marches (Dutch: Groepsmedaille van der Vierdaagse) is a non wearable bronze presentation medal awarded to each registered
Group Medal of the Four Day Marches
Group_Medal_of_the_Four_Day_Marches
Topics referred to by the same term
The Four may refer to: Glasgow Four, the four prominent leaders of the Glasgow School Four (comics), a group of comic book supervillains from the series
The_Four
Monthly football magazine
Total Football into FourFourTwo. In 2008 FourFourTwo entered into a three-year shirt sponsorship deal with Swindon Town. FourFourTwo has a number of annual
FourFourTwo
Mythological creatures in Chinese constellations
source needed] In the Digimon franchise, the Four Holy Beasts are a group of Digimon designed after the Four Symbols. Qinglongmon debuted in the anime Digimon
Four_Symbols
Public sculpture by Jean Dubuffet
Group of Four Trees is an abstract outdoor sculpture completed in 1972 by the French artist Jean Dubuffet. Commissioned by the American banker David Rockefeller
Group of Four Trees (Jean Dubuffet)
Group_of_Four_Trees_(Jean_Dubuffet)
Association football tournament in Mexico
into the four groups, which had their locations defined in advance: Group 1 being staged in Mexico City, Group 2 in Puebla and Toluca, Group 3 in Guadalajara
1970_FIFA_World_Cup
Military unit
Commander, Carrier Strike Group FOUR (CCSG-4 or COMSTRKGRUFOUR) is the U.S. Fleet Forces Command formation charged with training and certifying Atlantic
Commander Strike Force Training Atlantic
Commander_Strike_Force_Training_Atlantic
Group of transformations under which the object is invariant
chiral four-bladed pinwheel, and C5, C6, etc. are the symmetry groups of similar chiral pinwheels with five, six, etc. arms. D1 is the 2-element group containing
Symmetry_group
Topics referred to by the same term
(disambiguation) Four Asian Tigers: the economies of Hong Kong, Singapore, South Korea and Taiwan Four group (disambiguation) Gang of 14, a bipartisan group of U
Gang_of_Four_(disambiguation)
Topics referred to by the same term
Four may refer to: The Fearless Four (group), an American old school hip-hop group The Fearless Four (film), a 1997 animated film The Fearless Four,
The_Fearless_Four
Association football tournament in West Germany
competition once again began with the sixteen teams divided into four groups of four teams, the eight teams which advanced did not enter a knockout stage
1974_FIFA_World_Cup
Group in which the order of every element is a power of p
cyclic group C4 and the Klein four-group V4 are both 2-groups of order 4, but they are not isomorphic. Nor need a p-group be abelian; the dihedral group Dih4
P-group
10th European association football championship
addition of two extra groups in the group stage, and an extra round in the knockout phases. The four groups (A to D) still contained four teams each, with
UEFA_Euro_1996
South Korean girl group
4L (Korean: 포엘, short for Four Ladies) was a South Korean girl group formed in 2014 by Jade Contents Media. The group debuted on August 1, 2014, with
4L_(group)
Section of the British Labour Party's constitution concerning economic views
succeeded in ending its control by the Militant group in 1975. However, the attempt of the Clause Four group to oppose Militant in the Labour Party Young
Clause_IV
Mathematical connection between field theory and group theory
group is isomorphic to the Klein four-group. In the modern approach, one starts with a field extension L/K (read "L over K"), and examines the group of
Galois_theory
Group for which a given group is a normal subgroup
to group isomorphism, only four groups of order 8 {\displaystyle 8} containing a normal subgroup of order 2 {\displaystyle 2} with quotient group isomorphic
Group_extension
Theorem on the orders of subgroups
In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Orthogonal group of an indefinite quadratic form
mathematics, the indefinite orthogonal group, O ( p , q ) {\displaystyle \operatorname {O} (p,q)} is the Lie group of all linear transformations of an
Indefinite_orthogonal_group
Proto-psychological theory
The four temperament theory is a proto-psychological theory which suggests that there are four fundamental personality types: sanguine, choleric, melancholic
Four_temperaments
Bijective group homomorphism
group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group
Group_isomorphism
Vector in relativity
The Lorentz group may be represented by a set of 4 × 4 matrices Λ. The action of a Lorentz transformation on a general contravariant four-vector X (like
Four-vector
Lie group of Lorentz transformations
is a Lie group, the Lorentz group O(1, 3) is a group and also has a topological description as a smooth manifold. As a manifold, it has four connected
Lorentz_group
Topics referred to by the same term
Four Heavenly Kings of Orochi from The King of Fighters Four Heavenly Kings is a group of four powerful Bishoku-ya in the manga Toriko The Elite Four
Four Heavenly Kings (disambiguation)
Four_Heavenly_Kings_(disambiguation)
2025 Marvel Studios film
The Fantastic Four: First Steps is a 2025 American superhero film based on the Marvel Comics superhero team the Fantastic Four. Produced by Marvel Studios
The Fantastic Four: First Steps
The_Fantastic_Four:_First_Steps
Association football tournament in Sweden
1954: 16 teams still competed in four groups of four, but this time each team played each of the other teams in its group at least once, without extra time
1958_FIFA_World_Cup
Indian multinational conglomerate
The Tata Group (/ˈtɑːtɑː/) is an Indian multinational conglomerate headquartered in Mumbai. Established in 1868, it is India's largest conglomerate. Tata
Tata_Group
American contemporary Christian vocal quartet
Cherie Paliotta (later Cherie Adams) replaced Hassman in the group. Adams recorded four albums with Avalon: In a Different Light (1999), Joy: A Christmas
Avalon_(American_group)
American rhythm and blues band
drums) in 1954. The Four Lovers achieved minor success before a name change to The Four Seasons in 1960. During those five years, the group members also included
The_Four_Lovers
2010 British film directed by Chris Morris
Four Lions is a 2010 British political satire black comedy film directed by Chris Morris (in his directorial debut) from a screenplay written by Morris
Four_Lions
Instrumental and/or vocal music group
A musical ensemble, also known as a music group, musical group, or band, is a group of people who perform instrumental and/or vocal music, with the ensemble
Musical_ensemble
American vocal quartet
The Four Tops are an American vocal group formed in Detroit, Michigan, in 1953 as the Four Aims. They were one of the most commercially successful American
Four_Tops
Football championship
team from each pot was drawn into each of the four groups. The draw also determined which place in the group teams in pots 2–4 would take (e.g. A2, A3 or
UEFA_Euro_2012
Canadian headquartered international hotel chain
It was acquired by Anbang Insurance Group from the Blackstone Group for $359.7 million in 2016. In 1992, Four Seasons acquired Regent Hotels & Resorts
Four Seasons Hotels and Resorts
Four_Seasons_Hotels_and_Resorts
Non-abelian group of order eight
is isomorphic to the Klein four-group V. The full automorphism group of Q8 is isomorphic to S4, the symmetric group on four letters (see Matrix representations
Quaternion_group
May 2008 in four different venues. Sixteen teams participated in qualification in four groups containing four teams each. The four group winners joined
2008 AFC Challenge Cup qualification
2008_AFC_Challenge_Cup_qualification
2018–2019 edition of the UEFA Nations League
teams for the qualifying group stage of UEFA Euro 2020, and awarded berths in the play-offs, which decided four of the twenty-four final tournament slots
2018–19_UEFA_Nations_League
International football competition
matches within their group, except for one group in League D which played four, using the home-and-away round-robin format in June (four matchdays) and September
2022–23_UEFA_Nations_League
Type of symmetry group
for group 1, three for groups 2, 3, and 4, and four for groups 5, 6, and 7. For two of the seven frieze groups (groups 1 and 4) the symmetry groups are
Frieze_group
Line of alcoholic drinks
Four Loko is a line of alcoholic beverages sold by Phusion Projects of Chicago, Illinois, United States. Four Loko's previous recipe included caffeine
Four_Loko
Swiss watchmaker
manufacturers "Annual Report 2024" (PDF). Swatch Group. Retrieved 28 August 2025. Thompson, Joe (10 October 2017). "Four Revolutions: Part 1: A Concise History
The_Swatch_Group
Late 2000s German pop group
beFour was a German Eurodance group founded in Cologne. They have had a string of hits stretching from 2007 until 2009. The band's repertoire contains
BeFour
Commutative group in which all nonzero elements have the same order
Klein four-group. In the group generated by the symmetric difference on a (not necessarily finite) set, every element has order 2. Any such group is necessarily
Elementary_abelian_group
South Korean boy band
abbreviation for Twenty Four Seven With Us) is a South Korean boy band formed and managed by Pledis Entertainment. The group consists of six members:
TWS_(group)
Association football tournament in Scotland
or 9 groups consisting of 4 or 5 teams. The groups were seeded into two sets with the top 16 teams in Division One making up the first four groups, guaranteeing
Scottish_League_Cup
Central atom with four substituents located at the corners of a tetrahedron
all four groups attached to this carbon are on one side of a plane. The carbon atom lies at or near the apex of a square pyramid with the other four groups
Tetrahedral molecular geometry
Tetrahedral_molecular_geometry
Association football competition
teams were divided into four leagues, with Leagues A, B and C featuring sixteen teams each, divided into four groups of four teams. League D featured
2020–21_UEFA_Nations_League
Topics referred to by the same term
fraternity also known as the Four Brothers Quatre frères, a French ship The Brothers Four, an American folk singing group This disambiguation page lists
Four_Brothers
Ice hockey tournament group stage
Group A was one of two groups of the 2026 IIHF World Championship. The four best-placed teams advanced to the playoff round, while the last placed team
2026 IIHF World Championship Group A
2026_IIHF_World_Championship_Group_A
African Americans falsely accused of rape in 1949
The Groveland Four (or the Groveland Boys) were four African American teens, Ernest Thomas, Charles Greenlee, Samuel Shepherd, and Walter Irvin. In July
Groveland_Four
Causes movement in the hip
divided into four groups according to their orientation around the hip joint: the gluteal group; the lateral rotator group; the adductor group; and the iliopsoas
Muscles_of_the_hip
Football tournament qualification stage
four groups, from which the group winners qualify for the World Cup finals. The winner of the Qualifying Playoffs between the Runners-up of each four
2003 FIFA Women's World Cup qualification (UEFA)
2003_FIFA_Women's_World_Cup_qualification_(UEFA)
Device used to brew espresso coffee
machines were steam types, produced when a common boiler was piped to four group heads so that multiple types of coffee could be made at the same time
Espresso_machine
Islamic legal schools of law
emerged. One interpretation is that Sunni Islam was categorised into four groups: the Hanafites, Malikites, Shafi'ites, and Zahirites. Later, the Hanbalites
Madhhab
Association football tournament in Spain
rounds of group stages. It was also the third time (after 1934 and 1966) that all four semi-finalists were European. In the first round of Group 3, Hungary
1982_FIFA_World_Cup
American folk group
The Brothers Four is an American folk singing group formed in 1957 in Seattle, Washington, and best known for their 1960 hit song "Greenfields". Bob Flick
The_Brothers_Four
Cardinality of a mathematical group, or of the subgroup generated by an element
does not hold for composite orders, e.g. the Klein four-group does not have an element of order four. This can be shown by inductive proof. The consequences
Order_(group_theory)
North American association football tournament
the group stage. Prior to the 2012–13 season, the competition had involved four groups of four, with one Mexican team and one U.S. team in each group. A
CONCACAF_Champions_Cup
British electronic musician and DJ (born 1977)
Telegraph Media Group, 28 May 2005, www.telegraph.co.uk/culture/music/3642767/Make-it-funky-make-it-folky.html. "First/Last Party On Earth 07 - Four Tet". Soundcloud
Four_Tet
Financial data and software company
ION Group, also known as Ion and Ion Investment Group, is a financial data and software company headquartered in London. The company has expanded rapidly
ION_Group
and Tigray. Together these four groups make up three-quarters of the population. The country also has Omotic ethnic groups who speak Afro-Asiatic languages
List of ethnic groups in Ethiopia
List_of_ethnic_groups_in_Ethiopia
Second tier of the IIHF World Championships
2001 from Pool B and the top four Pool C teams. Beginning in 2012 the two groups became tiered rather than parallel. Group A teams were the nations who
IIHF World Championship Division I
IIHF_World_Championship_Division_I
The Four Larks were an R&B group that recorded from the 1960s through to the 1970s on various record labels. Their singles have been released on at least
The Four Larks (Philadelphia group)
The_Four_Larks_(Philadelphia_group)
Football tournament
The group stage was then played among only 16 teams in four groups of four, each group in a single host country, with the top two teams in each group advancing
UEFA_Women's_Champions_League
Ancient Chinese classification of occupations
classification of four occupations as Ban Gu understood it did not exist until the 2nd century BC. Ban explained the social hierarchy of each group in descending
Four_occupations
South Korean co-ed music group
stylized in all caps) is a South Korean co-ed group formed by DSP Media. The group consists of four members: J.Seph, BM, Somin, and Jiwoo. They officially
Kard_(group)
1993 disease outbreak
wastes or radioactivity for causing the outbreak. A group of UNM biologists studying deer mice near the Four Corners region at the time noticed that their population
1993 Four Corners hantavirus outbreak
1993_Four_Corners_hantavirus_outbreak
Classification based on antibodies and antigens on RBC surfaces
classified into four groups: those with antigen A (group A), those with antigen B (group B), those with both antigen A and B (group AB), and those with
Blood_type
Topics referred to by the same term
categories Four-Star Spectacular, a 1970s comic book series 4-Star, a ZX spectrum game by J. K. Greye Software Four Star Mary, an alternative rock group formed
Four_star
British boy band
but without Brown. The group continued with only four members, but decided to keep the name Five. Alongside other musical groups, Five were featured in
Five_(group)
South Korean girl group
K-pop group to enter the US Billboard Hot 100 and UK Singles Chart, within four months of debut. Furthermore, it made them the first K-pop girl group to
Fifty_Fifty_(group)
Proposed council of World War II allies
The "Four Policemen" was a postwar council with the Big Four that U.S. president Franklin D. Roosevelt proposed as a guarantor of world peace. Their members
Four_Policemen
FOUR GROUP
FOUR GROUP
Boy/Male
Tamil
Chaturbahave | சதà¯à®°à¯à®ªà®¹à®¾à®µà¯‡
Four-armed
Chaturbahave | சதà¯à®°à¯à®ªà®¹à®¾à®µà¯‡
Boy/Male
Bengali, French, Hebrew, Indian
Fair; Red; White
Girl/Female
Indian, Punjabi, Sikh
Tears of Eyes
Boy/Male
Tamil
Chaturbahu | சதà¯à®°à¯à®ªà®¾à®¹à¯Â
Four armed
Chaturbahu | சதà¯à®°à¯à®ªà®¾à®¹à¯Â
Biblical
four
Boy/Male
Indian, Sanskrit
Four Legged; Another Name for Tortoise
Boy/Male
Muslim/Islamic
Light
Boy/Male
Hindu, Indian, Kannada, Telugu, Traditional
Four Armed
Girl/Female
Indian, Telugu
Four Types
Male
Icelandic
Icelandic form of Old Norse Friðþjófr, FRIÃÞJÓFUR means "peace-thief."
Boy/Male
Scottish
From the water.
Boy/Male
African, Arabic, Australian, Lebanese
Light
Boy/Male
Native American
Four bears.
Boy/Male
Hindu, Indian, Punjabi, Sikh
Princess
Boy/Male
Hindu, Indian, Traditional
Four Faced; Another Name for Brahma
Boy/Male
Biblical
Four.
Boy/Male
Hindu
Four-armed
Boy/Male
Hindu, Indian
Four Faced; A Name for Varuna
Boy/Male
African
Rock.
Boy/Male
Australian, Japanese
Four Seasons
FOUR GROUP
FOUR GROUP
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Born of Fire
Girl/Female
Indian, Punjabi, Sikh
Attachment to Illumination
Surname or Lastname
English (Devon)
English (Devon) : habitational name from a place in Devon named Foxworthy, probably from an Old English personal name Færoc + Old English worðig ‘enclosure’.
Girl/Female
Australian, British, English, French, Greek, Hebrew, Irish, Welsh
Shining; Brightness; Nymph; Torch; Moon; Moon Elope; Variant of Helen
Boy/Male
Indian, Telugu
Beautiful; Veda; Name of Lord Krishna
Boy/Male
Indian
First rose
Boy/Male
Arabic, Muslim
Abundant; Copious
Male
English
English variant spelling of French Antoine, possibly ANTUAN means "invaluable."Â
Girl/Female
Muslim
Result of deeds, Way
Boy/Male
Tamil
Pratamesh | பà¯à®°à®¤à®¾à®®à¯‡à®·Â
Lord God, Lord Ganesh, Lord of the best
FOUR GROUP
FOUR GROUP
FOUR GROUP
FOUR GROUP
FOUR GROUP
superl.
Loathsome; disgusting; as, a foul disease.
n.
A naval vessel carrying seventy-four guns.
n.
A vehicle having four wheels.
superl.
Covered with, or containing, extraneous matter which is injurious, noxious, offensive, or obstructive; filthy; dirty; not clean; polluted; nasty; defiled; as, a foul cloth; foul hands; a foul chimney; foul air; a ship's bottom is foul when overgrown with barnacles; a gun becomes foul from repeated firing; a well is foul with polluted water.
n.
The sum of four units; four units or objects.
a.
Allowing passage in either of four directions; as, a four-way cock, or valve.
n.
A symbol representing four units, as 4 or iv.
a.
Hard; inflexible; obstinate; sour in aspect; hardy; bold.
n.
Four things of the same kind, esp. four horses; as, a chariot and four.
v. t.
To grind and bolt; to convert into flour; as, to flour wheat.
n.
See Foul ball, under Foul, a.
superl.
Scurrilous; obscene or profane; abusive; as, foul words; foul language.
v. t.
To macerate, and render fit for plaster or mortar; as, to sour lime for business purposes.
superl.
Disagreeable; unpleasant; hence; cross; crabbed; peevish; morose; as, a man of a sour temper; a sour reply.
n.
Strips of dressed skins with fur, used on garments for warmth or for ornament.
a.
Having four wheels.
v. t.
To sprinkle with flour.
a.
Having four corners or angles.
superl.
Cold and unproductive; as, sour land; a sour marsh.
n.
Fixed or appointed time; conjuncture; a particular time or occasion; as, the hour of greatest peril; the man for the hour.