Category:Group theory

A

• + Abelian group theory (1)
• + Algebraic groups (3)
• + Group automorphisms (0)

C

• + Combinatorial group theory (0)
• + Computational group theory (0)

D

• + Discrete groups (0)

F

• + Finite groups (2)
• + Functional subgroups (0)

G

• + Geometric group theory (0)
• + Group theorists (0)

I

• + Infinite group theory (0)

L

• + Lie groups (10)

M

• + Moonshine theory (0)

O

• + Ordered groups (0)

P

• + Permutation groups (1)
• + Properties of groups (0)

R

• + Representation theory (3)
• + Representation theory of groups (2)

• List of group theory topics
• Glossary of group theory

*

• Group theory

A

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

B

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

C

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

C cont.

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

D

• Diagonal subgroup
• Dihedral group
• Direct sum of groups
• Discrete logarithm
• Double coset

E

• Ehlers group
• Elementary group theory
• Elliptic curve
• Embedding problem
• Engel group
• Erlangen program
• Euclidean plane isometry
• Even and odd permutations
• Examples of groups
• Extensible automorphism
• Extension problem

F

• Family automorphism
• Fitting length
• 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

• Gain group
• Galois group
• Galois theory
• Generalized n-gon
• Generating set of a group
• Golod–Shafarevich theorem
• Group (mathematics)
• Group action
• Group cohomology
• Group extension
• Group homomorphism
• Group isomorphism
• Group isomorphism problem
• Group object
• Group of Lie type

H

• HN group
• HNN extension
• Hall–Janko graph
• Hamiltonian group
• Heisenberg group
• Herzog–Schönheim conjecture
• Hidden subgroup problem
• Higman–Sims graph
• Holomorph (mathematics)
• Hurwitz's automorphisms theorem

I

• IA automorphism
• Idempotent measure

I cont.

• Imperfect group
• Index calculus algorithm
• Induced representation
• Inner automorphism
• Iwasawa group

K

• Krull-Schmidt theorem

L

• 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
• Loop braid group
• Lovász conjecture
• Lyndon–Hochschild–Serre spectral sequence

M

• Maximal subgroup
• 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

• Newton's identities
• Nilpotent group
• Norm (group)
• Normal subgroup
• Number

O

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

P

• P-compact group
• P-group
• Perfect core
• Perfect group
• Periodic group
• Point group
• Point groups in three dimensions
• Point groups in two dimensions
• Polycyclic group
• Power automorphism
• Power closed
• Powerful p-group
• Principal homogeneous space
• Principal ideal theorem
• Product of group subsets

Q

• Quasigroup
• Quasisimple group
• Quaternion group
• Quotient group

R

• Real tree
• Reflection group
• Regular p-group
• Representation ring
• Retract (group theory)
• Root group