 List of group theory topics

Structures and operations
Basic properties of groups
 Butterfly lemma
 Center of a group
 Centralizer and normalizer
 Characteristic subgroup
 Commutator
 Composition series
 Conjugacy class
 Conjugate closure
 Conjugation of isometries in Euclidean space
 Core (group)
 Coset
 Derived group
 Elementary group theory
 Euler's theorem
 Fitting subgroup
 Generalized Fitting subgroup
 Hamiltonian group
 Identity element
Group homomorphisms
 Automorphism
 Automorphism group
 Factor group
 Fundamental theorem on homomorphisms
 Group homomorphism
 Group isomorphism
 Homomorphism
 Isomorphism theorem
 Inner automorphism
 Order automorphism
 Outer automorphism group
 Quotient group
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
 Abelian variety
 Algebraic group
 BanachTarski paradox
 Category of groups
 Dimensional analysis
 Elliptic curve
 Galois group
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
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
Computational group theory
 Coset enumeration
 Schreier's subgroup lemma
 Schreier–Sims algorithm
 Todd–Coxeter algorithm
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
 HerzogSchönheim 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)
Group theorists
 P. Hall
 G. Higman
 D. Hilbert
 O. Hölder
 B. Huppert
 K. Iwasawa
 Z. Janko
 C. Jordan
 F. Klein
 A. Kurosh
 J.L. Lagrange
 O. Schreier
 I. Schur
 R. Steinberg
 M. Suzuki
 L. Sylow
 J. Thompson
 J. Tits
 Helmut Wielandt
 H. Zassenhaus
 M. Zorn
See also
Categories: Mathematicsrelated lists
 Abstract algebra
 Group theory
 Properties of groups
 Outlines
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