List of group theory topics.html



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

• Classification of finite simple groups

Permutation and symmetry groups

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

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

Algebraic structures related to groups

Group representations

See also: list of 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

Computational group theory

• Coset enumeration
• Schreier's subgroup lemma
• Schreier-Sims algorithm
• Todd-Coxeter algorithm

Applications

• Computer algebra system
• Cryptography
  • Discrete logarithm
  • Triple DES
  • Caesar cipher
• 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

Major contributors to group theory