List of group theory topics
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.''This is a hidden deliberate self-link , so that changes to the list show up in Related Changes for this page.''
See also: List of abstract algebra topics, List of category theory topics
History, major contributors
- Joseph-Louis Lagrange
- Niels Abel
- Evariste Galois
- Augustin Louis Cauchy
- Arthur Cayley
- Otto Ludwig Hölder
- Camille Jordan
- Ludwig Sylow
- Ferdinand Georg Frobenius
- Sophus Lie
- Felix Klein
- William Burnside
- Richard Dedekind
- David Hilbert
- Max August Zorn
- John Thompson
- Martin Dunwoody
- John Conway
Famous problems
- Classification of finite simple groups
- Word problem for groups
- Subset sum problem
- Burnside's problem
- Whitehead problem
Applications
- Computer algebra system
- Exponentiating by squaring
- Knapsack problem
- Shor's algorithm
- Cryptography
- Standard Model
Definitions in common with other mathematical ideas
- Binary operation
- Bilinear operator
- Commutative
- Associativity
- Equivalence relation
- Equivalence class
- Bijection
- Multiplication table
- Lattice
- Up to
- Congruence relation
- Prime number
Mathematical objects which have (or make use of) a group operation
- Number
- Real number
- Integer
- Modular arithmetic
- Matrix
- Tensor
- Quaternion
- Hilbert space
- Pauli matrices
- Banach-Tarski paradox
- Galois group
- Dimensional analysis
- Lie group
- Algebraic group
- Elliptic curve
- Abelian variety
- Group object
Abstract algebra
- Quasigroup
- Semigroup
- Monoid
- Monoid ring
- Module
- Ring (algebra)
- Finite field
- Field
- Vector space
- Linear algebra
- Galois theory
Other mathematical disciplines which make great use of groups
- Geometry
- Algebraic geometry
- Algebraic topology
- Topological group
- Fundamental group
- Discrete space
- Homology
- Minkowski's theorem
Basic properties of groups and subgroups
- Elementary group theory
- Identity element
- Reciprocal
- Subgroup
- Coset
- Theorem of Lagrange
- Euler's theorem
- Normal subgroup
- Hamiltonian group
- Characteristic subgroup
- Torsion subgroup
- Centralizer and normalizer
- Stabilizer subgroup
- Center of a group
- Commutator
- Derived group
- Conjugate
- Conjugacy class
- Conjugate closure
- Core (group)
Group homomorphisms
- Automorphism
- Automorphism group
- Group homomorphism
- Group isomorphism
- Factor group
- Quotient group
- Homomorphism
- Order automorphism
- Isomorphism theorem
- Fundamental theorem on homomorphisms
- Inner automorphism
Basic group structures and operations
- Generating set of a group
- Sylow theorem
- Product of groups
- Direct product
- Direct sum
- Direct sum of groups
- Subdirect sum
- Semidirect product
- Group Extension
- Group cohomology
- Wreath product
- Free product
- Free group
- Free abelian group
- Presentation of a group
Basic building block of groups, and classifications
- P-group
- Cyclic group
- Abelian group
- Nilpotent group
- Solvable group
- Dihedral group
- Klein four-group
- Group representation
- Pro-finite group
- List of small groups
- Finitely generated abelian group
- Divisible group
Simple groups and their classification
- Simple group
- Symmetric group
- Alternating group
- General linear group
- Special linear group
- Mathieu group
- Janko group
- Conway group
- Fischer group
- Baby Monster group
- Monster group
- Bimonster
- Lie group
- Simple Lie group
- Weyl group
- Algebraic group
- Chevalley group
Understanding groups as permutation and symmetry groups
- Rubik's Cube
- Symmetry
- Symmetry group
- Euclidean group
- Frieze group
- Wallpaper group
- Crystallographic group
- Homogeneous space
- Permutation
- Even permutation
- Permutation group
- Group action
- Cayley's Theorem
- Orbit (mathematics)
- Burnside's lemma
- Steiner system
Group representations
