List of group theory topics
This page collects all articles on group theory, 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 order is by no means ideal; but it may help to provide some framework for a re-editing of the main topic. Nor are the entries below considered a definitive set of topics; rather they reflect the current state of group theory articles on Wikipedia. Feel free to add or subtract from this list as appropriate.
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
- Discrete logarithm
- Triple DES
- Caesar cipher
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
- Natural number
- Dimensional analysis
- Manifold
- Lie group
- Algebraic group
- Elliptic curve
- Abelian variety
Category theory etc.
- Morphism
- Topos
- Groupoid
- Limit (category theory)
- Preadditive category
- Initial object
- Yoneda lemma
- Natural transformation
- Embedding
- Standard Model
Abstract algebra
- Abstract algebra
- Universal algebra
- Algebra
- Subalgebra
- Quasigroup
- Semigroup
- Monoid
- Monoid ring
- Module
- Ring (algebra)
- Finite field
- Field
- Vector space
- Linear algebra
- Galois theory
- Galois group
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
- 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
- Janko group
- Conway group
- Monster group
- Bimonster
- Lie group
- Algebraic group
- Chevalley group
Understanding groups as permutation groups