Category:Group theory

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Group theory

In mathematics, a group is a set, together with a binary operation satisfying certain axioms, detailed in the group article.

Group theory is that branch of mathematics concerned with the study of groups.

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Subcategories

There are 17 subcategories to this category shown below (more may be shown on subsequent pages).

A Abelian group theory Algebraic groups Group automorphisms C Combinatorial group theory Computational group theory

D Discrete groups F Finite groups Functional subgroups G Geometric group theory Group theorists L Lie groups

M Moonshine theory O Ordered groups P Permutation groups Properties of groups R Representation theory Representation theory of groups

Pages in category "Group theory"

There are 183 pages in this section of this category.

List of group theory topics * Group theory Glossary of group theory A Absolutely simple group Additive identity Affine group Artin group B (B, N) pair Baby-step giant-step Bad group Banach–Tarski paradox Bianchi group Bicommutant Bimonster Bol loop Braid group Bruhat–Tits building Burnside theorem Burnside's lemma Burnside's problem C C closed subgroup CEP subgroup Caesar cipher Cartan-Dieudonné theorem Category of abelian groups Category of groups Cayley graph Cayley's theorem Center (group theory) Central extension Centralizer and normalizer Character group Characteristic subgroup Characteristically simple group Cherlin-Zilber conjecture Circle group Class automorphism Class function Classification of finite simple groups Commensurability (mathematics) Commutant Commutator Commutator subgroup Complete group Complex reflection group Component (group theory) Composition series Congruence subgroup Conjugacy class Conjugacy class sum Conjugate closure Conjugation of isometries in Euclidean space Conway's orbifold notation Core (group) Coset Coset enumeration Coxeter group Cremona group Crystallographic group Crystallographic restriction theorem Cycle graph (algebra)

D Diagonal subgroup Dihedral group Direct sum of groups Discrete logarithm Double coset E Elementary amenable group Elementary group theory Elliptic curve Erlangen program Euclidean plane isometry Even and odd permutations Examples of groups Extensible automorphism Extension problem F FC group Family automorphism Fitting's theorem Fixed points of isometry groups in Euclidean space Frattini subgroup Frattini's argument Free group Free product Frieze group Fully normalized subgroup Fundamental theorem of Galois theory G Galois group Galois theory Generating set of a group Golod-Shafarevich theorem Group (mathematics) Group cohomology Group extension Group homomorphism Group isomorphism Group object Group of Lie type Growth rate (group theory) H HN group HNN extension Hall's universal group Hall–Janko graph Hamiltonian group Heisenberg group Herzog-Schönheim conjecture Hidden subgroup problem Higman's embedding theorem Higman–Sims graph Holomorph (mathematics) Hurwitz's automorphisms theorem I IA automorphism Imperfect group Index calculus algorithm Induced representation Infinite conjugacy class property Inner automorphism K Krull-Schmidt theorem L Landau's function Latin square property Lattice of subgroups Leech lattice Length function Linear group

L cont. List of finite simple groups List of spherical symmetry groups Locally finite group Loop braid group Lovász conjecture M Maximal subgroup Modular arithmetic Modular group Molien series Monstrous moonshine Moufang loop Multiplicative group Multiplicative group of integers modulo n N Newton's identities Norm (group) Normal core Normal series Normal subgroup Number O One-dimensional symmetry group Order (group theory) Outer automorphism group P P-compact group P-group Periodic group Point group Point groups in three dimensions Point groups in two dimensions Power automorphism Power closed Powerful p-group Principal homogeneous space Principal ideal theorem Pro-finite group Pro-p group Product of group subsets Prüfer rank Q Quasigroup Quasisimple group Quaternion group Quotient group R Radical of an algebraic group Real tree Reflection group Residually finite Residue class-wise affine group Retract (group theory) Root group S Schnorr group Schoof's algorithm Schoof-Elkies-Atkin algorithm Schottky group Schreier refinement theorem Schreier's subgroup lemma Schur multiplier Schur-Zassenhaus theorem Scott core theorem Section (mathematics) Semidirect product Serre's property FA

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Category: Abstract algebra

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