In mathematics, a group is a set, together with a binary operation satisfying certain axioms, detailed in the above article. The branch of mathematics which studies groups is called group theory.

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

Subcategories

There are 12 subcategories to this category.

Abelian group theory C Computational group theory D Discrete groups F Finite groups

G Geometric group theory Group theorists L Lie groups M Moonshine theory P Permutation groups

R Representation theory Representation theory of groups T Topological groups

Articles in category "Group theory"

There are 161 articles in this category.

Abelian group Advanced modular arithmetic theory Affine group Amenable group Artin group B BN pair Baby-step giant-step Bad group Banach-Tarski paradox Bimonster Braid group Burnside's problem C Caesar cipher Category of abelian groups Category of groups Cayley graph Center of a group Central extension Centralizer and normalizer Character group Characteristic subgroup Class function Classification of finite simple groups Commensurable Commutant Complete group Composition series Congruence subgroup Conjugacy class Conjugate closure Core (group) Coset Coset enumeration Coxeter group Crystallographic group Cycle graph (group) Cyclic group D Derived group Diagonal subgroup Dicyclic group Dihedral group Direct sum of groups Discrete group Discrete logarithm Divisible group Double coset E Elementary group theory Elliptic curve Equivariant Erlangen program Even and odd permutations Examples of groups Extension (algebra)

F Feit-Thompson theorem Finite Finite group Finitely generated abelian group Fitting subgroup Frattini subgroup Free abelian group Free group Free product Free regular set Frieze group Frieze pattern Frobenius group G Galois group Galois theory Gell-Mann matrices Generating set of a group Geometric group theory Glossary of group theory Gromov's theorem on groups of polynomial growth Group (mathematics) Group action Group cohomology Group homomorphism Group isomorphism Group object Group of Lie type Group theory Growth rate (group theory) H Hall-Janko graph Hamiltonian group Heisenberg group Higman-Sims graph Hilbert space Hurwitz's automorphisms theorem Hyperbolic group I Index calculus algorithm Induced representation Infinite conjugacy class property Integer Integer partition L Landau's function Leech lattice Lie group Linear algebra Linearly ordered group List of finite simple groups List of group theory topics List of small groups M Maximal subgroup Modular group Modular representation theory Monstrous moonshine Multiplicative group

M cont. Multiplicative group of integers modulo n N Nilpotent group Normal series Normal subgroup Number O Order (group theory) Outer automorphism group P P-group PSL(2,7) Permutation group Presentation of a group Principal homogeneous space Pro-finite group Product of groups Prüfer rank Q Quasigroup Quasisimple group Quaternion group Quotient group R Radical of an algebraic group Rank of an abelian group Real tree S Schnorr group Schreier refinement theorem Schreier's subgroup lemma Schur multiplier Scott core theorem Semidirect product Simple group Solvable Solvable group Spectral sequence Strong generating set Subgroup Subgroup growth Subset sum problem Symmetric group System of imprimitivity T Tame group Tarski monster group Torsion subgroup Transfer (group theory) Transversal V Vector space W Wallpaper group Weyl group Whitehead problem Word metric Word problem for groups Wreath product Y Young symmetrizer Young tableau Z Zassenhaus group Zassenhaus lemma