Category:Group theory

A

• ► Abelian group theory‎ (1 C, 30 P)
• ► Algebraic groups‎ (3 C, 51 P)
• ► Group automorphisms‎ (8 P)

B

• ► Braid groups‎ (9 P)

C

• ► Combinatorial group theory‎ (17 P)
• ► Computational group theory‎ (10 P)
• ► Coxeter groups‎ (7 P)

D

• ► Discrete groups‎ (2 C, 23 P)

F

• ► Finite groups‎ (4 C, 108 P)

F cont.

• ► Functional subgroups‎ (9 P)

G

• ► Geometric group theory‎ (40 P)
• ► Group theorists‎ (105 P)

I

• ► Infinite group theory‎ (36 P)

L

• ► Lie groups‎ (10 C, 134 P)

M

• ► Moonshine theory‎ (7 P)

N

• ► Nilpotent groups‎ (2 P)

O

• ► Ordered groups‎ (13 P)

P

• ► P-groups‎ (18 P)

P cont.

• ► Permutation groups‎ (1 C, 29 P)
• ► Properties of groups‎ (1 C, 68 P)

R

• ► Reflection groups‎ (1 C, 2 P)
• ► Representation theory‎ (8 C, 124 P)
• ► Representation theory of groups‎ (4 C, 34 P)

S

• ► Solvable groups‎ (11 P)
• ► Subgroup properties‎ (40 P)
• ► Subgroup series‎ (8 P)

T

• ► Topological groups‎ (2 C, 42 P)

• Glossary of group theory
• Group (mathematics)
• Group theory
• List of group theory topics

2

• 2-group

A

• Absolutely convex set
• Absolutely simple group
• Additive identity
• Affine group
• Affine manifold
• Affine representation
• Artin group
• Automorphisms of the symmetric and alternating groups

B

• (B, N) pair
• Baby-step giant-step
• Banach–Tarski paradox
• Bass–Serre theory
• Bender's method
• Bianchi group
• Bicommutant
• Bimonster group
• Bol loop
• Braid group
• Buekenhout geometry
• Building (mathematics)
• Burnside ring
• Burnside theorem
• Burnside's lemma
• Burnside's problem

C

• C closed subgroup
• Caesar cipher
• Capable group
• Cartan–Dieudonné theorem
• Category of abelian groups
• Category of groups
• Cayley graph
• Cayley's theorem
• Center (group theory)
• Centralizer and normalizer
• CEP subgroup
• Character group
• Character table
• Characteristic subgroup
• Characteristically simple group
• Circle group
• User:Ckhenderson
• Class automorphism
• Class function
• Classification of finite simple groups
• CN-group
• Cohomological dimension
• Commutant
• Commutator
• Commutator subgroup
• Complement (group theory)
• Complex reflection group
• Component (group theory)
• Congruence subgroup
• Conjugacy class
• Conjugacy class sum
• Conjugacy problem
• Conjugate closure
• Conjugation of isometries in Euclidean space
• Core (group)
• Coset
• Coset enumeration
• Cosocle

C cont.

• Coxeter notation
• Cremona group
• Critical group
• Crystallographic restriction theorem
• Cycle graph (algebra)

D

• De Sitter invariant special relativity
• Demushkin group
• Diagonal subgroup
• Direct product of groups
• Direct sum of groups
• Discrete logarithm
• Double coset

E

• Ehlers group
• Elementary group theory
• Elliptic curve
• Embedding problem
• Engel group
• Erlangen program
• Esquisse d'un Programme
• Euclidean plane isometry
• Examples of groups
• Extensible automorphism

F

• Fesenko group
• Fitting's theorem
• Fixed points of isometry groups in Euclidean space
• Formation (group theory)
• Frattini subgroup
• Frattini's argument
• Free group
• Free partially commutative group
• Free product
• Frobenius determinant theorem
• Fully normalized subgroup
• Fundamental theorem of Galois theory

G

• G-module
• Gain group
• Galois group
• Galois theory
• Generalized dihedral group
• Generalized polygon
• Generating set of a group
• Golod–Shafarevich theorem
• Gorenstein–Harada theorem
• Grigorchuk group
• Group action
• Group cohomology
• Group extension
• Group homomorphism
• Group isomorphism
• Group isomorphism problem
• Group object
• Group of Lie type
• Group representation
• Grushko theorem

H

• Hajós's theorem
• Hall–Higman theorem
• Hall–Janko graph
• Hamiltonian group
• Hanna Neumann conjecture
• Heisenberg group
• Herzog–Schönheim conjecture
• Hidden subgroup problem
• Higman–Sims graph
• History of group theory
• HN group
• HNN extension
• Holomorph (mathematics)

H cont.

• Homeomorphism group
• Hopfian object
• Hurwitz's automorphisms theorem

I

• IA automorphism
• Idealizer
• Idempotent measure
• Imperfect group
• Index calculus algorithm
• Index of a subgroup
• Induced character
• Induced representation
• Infinite group
• Inner automorphism
• Iwasawa group

J

• Jordan–Schur theorem

K

• Krull–Schmidt theorem
• Kurosh subgroup theorem

L

• Lagrange's theorem (group theory)
• Landau's function
• Latin square property
• Lattice of subgroups
• Length function
• List of character tables for chemically important 3D point groups
• List of finite simple groups
• List of spherical symmetry groups
• Lorentz group
• Lovász conjecture
• Lyndon–Hochschild–Serre spectral sequence

M

• Matsumoto's theorem (group theory)
• Maximal subgroup
• Mennicke symbol
• Metabelian group
• Metacyclic group
• Metanilpotent group
• Modular arithmetic
• Modular group
• Monomial group
• Monstrous moonshine
• Moufang loop
• Multiplicative group
• Multiplicative group of integers modulo n

N

• N-group (category theory)
• Newton's identities
• Nilpotent group
• Norm (group)
• Normal subgroup
• Nottingham group
• Number

O

• One-dimensional symmetry group
• Opposite group
• Orbifold notation
• Order (group theory)
• Outer automorphism group

P

• P-compact group
• Parity of a permutation
• Perfect core
• Perfect group
• Periodic group
• Ping-pong lemma
• Point group
• Point groups in three dimensions
• Point groups in two dimensions
• Polycyclic group
• Power automorphism
• Power closed
• Powerful p-group