List of group theory topics
From Wikipedia, the free encyclopedia
[edit] 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]
- 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]
[edit] Group representations
See also: List of representation theory representation theory topics and List of harmonic analysis 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
- Nielsen transformation
- Tarski monster group
- Thompson groups
- Tietze transformation
- Transfer (group theory)
