List of group theory topics
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Structures and operations
[edit]- Conjugacy class sum
- Central extension
- Direct product of groups
- Direct sum of groups
- Extension problem
- Free abelian group
- Free group
- Free product
- Generating set of a group
- Group cohomology
- Group extension
- Presentation of a group
- Product of group subsets
- Schur multiplier
- Semidirect product
- Sylow theorems
- Wreath product
Basic properties of groups
[edit]- 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
- Euler's theorem
- Fitting subgroup
- Hamiltonian group
- Identity element
- Lagrange's theorem
- Multiplicative inverse
- Normal subgroup
- Perfect group
- p-core
- Schreier refinement theorem
- Subgroup
- Transversal (combinatorics)
- Torsion subgroup
- Zassenhaus lemma
Group homomorphisms
[edit]Basic types of groups
[edit]Simple groups and their classification
[edit]- Alternating group
- Borel subgroup
- Chevalley group
- Conway group
- Feit–Thompson theorem
- Fischer group
- General linear group
- Group of Lie type
- Group scheme
- HN group
- Janko group
- Lie group
- Linear algebraic group
- List of finite simple groups
- Mathieu group
- Monster group
- Projective group
- Reductive group
- Simple group
- Special linear group
- Symmetric group
- Thompson group (finite)
- Tits group
- Weyl group
Permutation and symmetry groups
[edit]- Arithmetic group
- Braid group
- Burnside's lemma
- Cayley's theorem
- Coxeter group
- Crystallographic group
- Crystallographic point group, Schoenflies notation
- Discrete group
- Euclidean group
- Even and odd permutations
- Frieze group
- Frobenius group
- Fuchsian group
- Geometric group theory
- Group action
- Homogeneous space
- Hyperbolic group
- Isometry group
- Orbit (group theory)
- Permutation
- Permutation group
- Rubik's Cube group
- Space group
- Stabilizer subgroup
- Steiner system
- Strong generating set
- Symmetry
- Symmetric group
- Symmetry group
- Wallpaper group
Concepts groups share with other mathematics
[edit]Mathematical objects making use of a group operation
[edit]Mathematical fields and topics making important use of group theory
[edit]Algebraic structures related to groups
[edit]Group representations
[edit]Computational group theory
[edit]Applications
[edit]Famous problems
[edit]Other topics
[edit]- Amenable group
- Capable group
- Commensurability (group theory)
- Compact group
- Compactly generated group
- Complete group
- Complex reflection group
- Congruence subgroup
- Continuous symmetry
- Frattini subgroup
- Growth rate
- Heisenberg group, discrete Heisenberg group
- Molecular symmetry
- Nielsen transformation
- Reflection group
- Tarski monster group
- Thompson groups
- Tietze transformation
- Transfer (group theory)
Group theorists
[edit]- N. Abel
- M. Aschbacher
- R. Baer
- R. Brauer
- W. Burnside
- R. Carter
- A. Cauchy
- A. Cayley
- J.H. Conway
- R. Dedekind
- L.E. Dickson
- M. Dunwoody
- W. Feit
- B. Fischer
- H. Fitting
- G. Frattini
- G. Frobenius
- E. Galois
- G. Glauberman
- D. Gorenstein
- R.L. Griess
- M. Hall, Jr.
- P. Hall
- G. Higman
- D. Hilbert
- O. Hölder
- B. Huppert
- K. Iwasawa
- Z. Janko
- C. Jordan
- F. Klein
- A. Kurosh
- J.L. Lagrange
- C. Leedham-Green
- F.W. Levi
- Sophus Lie
- W. Magnus
- E. Mathieu
- G.A. Miller
- B.H. Neumann
- H. Neumann
- J. Nielson
- Emmy Noether
- Ø. Ore
- O. Schreier
- I. Schur
- R. Steinberg
- M. Suzuki
- L. Sylow
- J. Thompson
- J. Tits
- Helmut Wielandt
- H. Zassenhaus
- M. Zorn