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.
Basic group structures and operations
Basic properties of groups
Group homomorphisms
Basic types of groups
Simple groups and their classification
Permutation and symmetry groups
- Associativity
- Bijection
- Bilinear operator
- Binary operation
- Commutative
- Congruence relation
- Equivalence class
- Equivalence relation
- Lattice (group)
- Lattice (discrete subgroup)
- Multiplication table
- Prime number
- Up to
Mathematical objects making use of a group operation
Mathematical fields & topics making important use of group theory
- Algebraic geometry
- Algebraic topology
- Discrete space
- Fundamental group
- Geometry
- Homology
- Minkowski's theorem
- Topological group
Group representations
- Affine representation
- Character theory
- Great orthogonality theorem
- Maschke's theorem
- Monstrous moonshine
- Projective representation
- Representation theory
- Schur's lemma
Computational group theory
Applications
- Computer algebra system
- Cryptography
- Exponentiating by squaring
- Knapsack problem
- Shor's algorithm
- Standard Model
Famous problems
- Burnside's problem
- Classification of finite simple groups
- Herzog-Schönheim conjecture
- Subset sum problem
- Whitehead problem
- Word problem for groups
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
- Nielsen transformation
- Tarski monster group
- Thompson groups
- Tietze transformation
- Transfer (group theory)
Major contributors to group theory
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