References for Group (mathematics)

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References to other articles, organized by section

Addition
Associative property
Binary operation
Classification of finite simple groups
Computational group theory
Évariste Galois
Finite group
Finitely generated group
Galois group
Generating set
Geometric group theory
Geometric shape
Geometric transformation
Geometry
Group representation
Group theory
Identity element
Infinite set
Integer
Inverse element
Lie group
Mathematical structure
Mathematics
Molecular symmetry
Number theory
Ordered pair
Particle physics
Poincaré group
Point group
Polynomial equation
Polynomial root
Quotient group
Representation theory
Rubik's Cube
Rubik's Cube group
Set (mathematics)
Simple group
Spacetime
Special relativity
Standard Model
Subgroup
Symmetries
Symmetry group
Zero of a function

First example: the integers

Addition
Associativity
Binary operation
Closure (mathematics)
Identity element
Integer
Inverse element
Summation
Zero

Definition

Binary operation
Element (mathematics)
Monster group
Richard Borcherds
Set (mathematics)

Notation and terminology

Abelian group
Abuse of notation
Automorphism group
Commutative
Field (mathematics)
Function (mathematics)
Function composition
Geometric transformation
Group axioms
Mathematical object
Multiplication
Ordered pair
Permutation group
Real number
Symmetry (mathematics)

Second example: a symmetry group

Cayley table
Congruence (geometry)
Coset
Diagonal
Dihedral group
Identity operation
Plane (geometry)
Reflection (mathematics)
Rotation (mathematics)
Square
Subgroup
Symmetry
Translation (geometry)

History

Abstract group
Algebra
Algebraic group
Armand Borel
Arthur Cayley
Augustin Louis Cauchy
Camille Jordan
Carl Friedrich Gauss
Class group
Classification of finite simple groups
Claude Chevalley
Daniel Gorenstein
Disquisitiones Arithmeticae
Élie Cartan
Equation solving
Erlangen program
Ernst Kummer
Évariste Galois
Felix Klein
Ferdinand Georg Frobenius
Fermat's Last Theorem
Finite group
Galois group
Hermann Weyl
Hyperbolic geometry
Issai Schur
Jacques Tits
John G. Thompson
Joseph-Louis Lagrange
Leopold Kronecker
Lie group
Locally compact group
Mathematical proof
Michael Aschbacher
Modular representation theory
Number theory
Paolo Ruffini (mathematician)
Permutation
Polynomial equation
Prime number
Projective geometry
Representation theory
Richard Brauer
Root of a function
Sophus Lie
Symmetry group
University of Chicago
Walter Feit
Walther von Dyck
William Burnside

Elementary consequences of the group axioms

Bracket
Mathematical induction

Division

Bijection

Equivalent definition with relaxed axioms

Left identity
Left inverse element
Semigroup

Basic concepts

Group homomorphism
Quotient by an equivalence relation
Quotient group
Subgroup
Subset

Group homomorphisms

Bijective
Category (mathematics)
Category of groups
Group isomorphism
Injective
Monomorphism

Subgroups

Generating set of a group
Lattice of subgroups
Necessary and sufficient conditions
Subgroup test

Cosets

Empty set
If and only if
Intersection (set theory)
Normal subgroup
Partition of a set
Union (set theory)

Quotient groups

Epimorphism
First isomorphism theorem
Semidirect product
Surjective
Universal property

Presentations

Cayley graph
Discrete group
Free group
Presentation of a group

Examples and applications

Abstract algebra
Algebraic geometry
Algebraic topology
Algorithm
Chemistry
Computational group theory
Computer science
Continuous function
Cryptography
Equivalence class
Functor
Fundamental group
Geometric group theory
Glossary of topology
Henri Poincaré
Homotopy
Hyperbolic group
Multiplicative group
Neighbourhood (mathematics)
Null-homotopic
Physics
Topological space
Wallpaper group
Winding number

Numbers

Algebra over a field
Module (mathematics)
Rational number
Ring (mathematics)
Vector space

Rationals

Division (mathematics)
Fraction (mathematics)
Rational number

Modular arithmetic

12-hour clock
Bézout's identity
Greatest common divisor
Modular arithmetic
Multiplicative group of integers modulo n
Public-key cryptography
Remainder
Representative (mathematics)

Cyclic groups

Center (group theory)
Clockwise
Commutator
Complex number
Field theory (mathematics)
Fundamental theorem of finitely generated abelian groups
Power (mathematics)
Primitive root modulo n
Root of unity
Vertex (graph theory)

Symmetry groups

(2,3,7) triangle group
Ammonia
Antiderivative
Buckminsterfullerene
CD player
Coding theory
Crystallography
Cubane
Curie temperature
Differential equation
Differential Galois theory
Ferroelectric
Forward error correction
Geometric invariant theory
Geometry
Goldstone boson
Group action (mathematics)
Hyperbolic geometry
Hyperbolic plane
Icosahedral symmetry
Invariant theory
Mathematical analysis
Mathieu group
Molecular symmetry
Octahedral symmetry
Phase transition
Phonon
Point group
Potassium tetrachloroplatinate
Quantum mechanics
Space group
Spontaneous symmetry breaking
Symmetry in mathematics
Tessellation

General linear group and representation theory

Compact group
Computer graphics
Dimension
Euclidean space
Group representation
Invertible matrix
Linear group
Matrix (mathematics)
Matrix group
Matrix multiplication
Rotation matrix
Special orthogonal group
Topological group
Vector (mathematics)

Galois groups

Cubic equation
Field extension
Fundamental theorem of Galois theory
Galois theory
Nth root
Quadratic equation
Quadratic formula
Quartic equation
Quintic equation
Solvable group
Splitting field

Finite groups

Cayley's theorem
Dihedral group of order 6
Divisor
Equilateral triangle
Factorial
Finite set
Lagrange's theorem (group theory)
Order of a group
Sylow theorems
Symmetric group

Finite abelian groups

Direct product
Fundamental theorem of finitely generated abelian groups
Lagrange's theorem (group theory)

Simple groups

Jordan–Hölder theorem
Simple group

Classification of finite simple groups

Classification theorems
Computer algebra system
Extension problem
List of finite simple groups
List of small groups
Modular function
Monster group
Monstrous moonshine
Richard Borcherds
Sporadic group
Sporadic groups

Groups with additional structure

Computer-aided proof
Existential quantifier
Group object
Morphism
Nullary operation
Unary operation

Topological groups

Adele ring
Category of topological spaces
Complex plane
Étale fundamental group
Fundamental theorem of Galois theory
Haar measure
Harmonic analysis
Krull topology
Local field
Locally compact topological group
Neighbourhood (mathematics)
P-adic number
Real line
Topological field
Topological space
Unit circle

Lie groups

Conserved quantities
Diffeomorphism
Differentiable manifold
Elementary particle
Fundamental force
Gauge theory
Gravitation
Local symmetry
Lorentz transformation
Mechanics
Minkowski space
Noether's theorem
Open subset
Poincaré group
Quantum field theories
Rotation
Smooth map
Space
Spacetime
Special relativity
Standard Model
Time

Generalizations

Abelian group
Arity
Associative property
Cancellation property
Category (mathematics)
Closure (mathematics)
Commutative monoid
Commutative property
Complex number
Fundamental groupoid
Grothendieck group
Groupoid
Identity element
Integer
Integers modulo n
Loop (algebra)
Magma (algebra)
Monoid
N-ary group
Natural number
Partial groupoid
Quasi-group
Quasigroup
Rational number
Real number
Semigroup
Semigroupoid
Small category
Stack (mathematics)
Unital magma

Source on Wikipedia (https://en.wikipedia.org)

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