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Finite group

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups.

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Overview

History

Examples

Main theorems

Number of groups of a given order

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Map overview Semantic statistics

Finite group

Nodes97
Edges96
Triples45
Avg. degree1.98
Density0.020619
Components1

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Finite group

Top relations

related to Groups of Lie type · 21
Finite group → Although, Camille Jordan's, Chevalley, Chevalley's, Claude Chevalley, Finite, Galois, In, Leonard Dickson, Lie, Mathieu, Moreover, Other, PSL, Ree, Special, Steinberg, Suzuki, The, This
related to history · 5
Finite group → As, Chevalley, During, One, Steinberg
related to Feit–Thompson theorem · 4
Finite group → It, The Feit, Thompson, WalterFeitandJohn Griggs Thompson
related to Burnside's theorem · 3
Finite group → Abelian, Burnside's, Hence
related to Lagrange's theorem · 3
Finite group → For, Joseph-Louis Lagrange, The
see also · 2
Finite group → Association, Classification
is a · 1
Finite group → group whose underlying set is finite

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Important terminology

groups finite group order theorem simple cyclic prime lie solvable number every type classification elements theory abelian isomorphism subgroup many

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Finite groupis agroup whose underlying set is finite0.90text
Chevalleyinstance ofmathematicians0.80text
Steinberg also increased the understanding of finite analogs of classical groupsinstance ofmathematicians0.80text
and other related groupsinstance ofmathematicians0.80text
theoretical physicsinstance ofThe properties of finite groups can thus play a role in subjects0.80text
chemistryinstance ofThe properties of finite groups can thus play a role in subjects0.80text
the Sylow theoremsinstance ofof results0.80text
Finite grouprelated to Burnside's theoremBurnside's0.60section
Finite grouprelated to Burnside's theoremHence0.60section
Finite grouprelated to Burnside's theoremAbelian0.60section
Finite grouprelated to Feit–Thompson theoremThe Feit0.60section
Finite grouprelated to Feit–Thompson theoremThompson0.60section

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