List of group theory topics
From Wikipedia, the free encyclopedia
This is a list of group theory topics, by Wikipedia page, to provide an overview of the topic and to allow those interested to use the "Related changes" feature to keep abreast of edits in this area.
See also: List of abstract algebra topics, List of category theory topics, list of Lie group topics.
[edit] Basic group structures and operations
[edit] Basic properties of groups
[edit] Group homomorphisms
[edit] Basic types of groups
[edit] Simple groups and their classification
[edit] Permutation and symmetry groups
[edit] Concepts groups share with other mathematics
- Associativity
- Bijection
- Bilinear operator
- Binary operation
- Commutative
- Congruence relation
- Equivalence class
- Equivalence relation
- Lattice (group)
- Lattice (discrete subgroup)
- Multiplication table
- Prime number
- Up to
[edit] Mathematical objects making use of a group operation
[edit] Mathematical fields & topics making important use of group theory
- Algebraic geometry
- Algebraic topology
- Discrete space
- Fundamental group
- Geometry
- Homology
- Minkowski's theorem
- Topological group
[edit] Algebraic structures related to groups
[edit] Group representations
See also list of harmonic analysis and representation theory topics
- Affine representation
- Character theory
- Great orthogonality theorem
- Maschke's theorem
- Monstrous moonshine
- Projective representation
- Representation theory
- Schur's lemma
[edit] Computational group theory
[edit] Applications
- Computer algebra system
- Cryptography
- Exponentiating by squaring
- Knapsack problem
- Shor's algorithm
- Standard Model
[edit] Famous problems
- Burnside's problem
- Classification of finite simple groups
- Herzog-Schönheim conjecture
- Subset sum problem
- Whitehead problem
- Word problem for groups
[edit] Other topics
- Amenable group
- Capable group
- Commensurability (mathematics)
- Compact group
- Compactly generated group
- Complete group
- Congruence subgroup
- Continuous symmetry
- Frattini subgroup
- Growth rate
- Heisenberg group, discrete Heisenberg group
- Molecular symmetry
- Tarski monster group
- Thompson groups
- Transfer (group theory)

