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Abelian Group
Adjoint
Adjoint Operator
Algebraic Integer
Algebraic Number
Algebraic Number Field
Algebraic Variety
Algebraically Closed
Alternating Group
Antipode
Ascending Chain Condition
Associates
Automorphism
Axis Of Rotation
Basechange Matrix
Basis
Bezout Bound
Bilinear Form
Bracket
Branch Points
Branched Covering
Cancellation Law
Canonical Map
Cayley Hamilton Theorem
Cayley's Theorem
Center
Centralizer
Characteristic
Characteristic Polynomial
Characteristic Zero
Class Equation
Class Group
Class Number
Column Space
Common Zeros
Commutative Ring
Commutator
Commutator Subgroup
Compact Group
Complete Set
Complex Algebraic Group
Congruence
Conics
Conjugacy Class
Conjugate
Conjugate Subgroup
Conjugation
Correspondence Theorem
Counting Formula
Covering Space
Crystallographic Point Group
Cusp
Cyclic Group
Cyclic Subgroup
Cyclotomic Field
Cyclotomic Polynomial
Degenerate
Degenerate Conic
Degree
Determinant
Diagonal Matrix
Diagonalizable
Dihedral Group
Dimension
Dimension Formula
Direct Sum
Discrete
Discrete Subgroup
Discriminant
Dot Product
Eigenvalue
Eigenvector
Eisenstein Criterion
Elementary Integer Matrix
Elementary Symmetric Functions
Equator
Equivalence Class
Equivalence Relation
Euclidean Algorithm
Euclidean Domain
Exceptional Groups
Extension Field
Faithful
Fiber
Field
Finite Dimensional
Finite Extension
Finite Field
First Isomorphism Theorem
First Sylow Theorem
Fixed Field
Fixed Field Theorem
Fixed Point Theorem
Fixed Vector
Fraction Field
Free
Free Abelian Group
Free Group
Free Module
Free Product
Free Semigroup
Function Field
Fundamental Thm Of Algebra
Fundamental Thm Of Arithmetic
Galois Extension Field
Galois Group
Gauss's Lemma
Gaussian Integers
Gaussian Prime
General Linear Group
Generalized Eigenvector
Generator
Gram Schmidt Orthonormalization
Greatest Common Divisor
Group
Group Character
Group Operation
Half Integer
Hermitian
Hermitian Form
Hermitian Space
Hermitian Symmetry
Hilbert Basis Theorem
Hilbert's Nullstellensatz
Homeomorphism
Homogeneous Polynomial
Homomorphism
Hypervector
Icosahedral Group
Ideal
Ideal Class
Idempotent
Identity
Identity Map
Inclusion Map
Indefinite
Index
Induced Law
Infinite Cyclic
Infinite Dimensional
Integral Domain
Intermediate Field
Invariants
Invertible Integer Matrix
Invertible Operator
Irreducible
Irreducible Character
Irreducible Factorization
Irreducible Representation
Isometry
Isomorphic
Isomorphism
Isomorphism Class
Jacobi Identity
Jordan Block
Jordan Canonical Form
Jordan Decomposition Theorem
Kernel
Klein Four Group
Kronecker Delta
Kronecker Weber Theorem
Kummer Extension
Lagrange's Theorem
Latitude
Lattice
Law Of Composition
Leading Coefficient
Left Coset
Lie Algebra
Lie Type
Linear Combination
Linear Group
Linear Operator
Linear Relation
Linear Transformation
Linearly Dependent
Linearly Independent
Longitude
Lorentz Group
Lorentz Transformations
Luroth's Theorem
Maschke's Theorem
Mathieu Group
Matrix Exponential
Matrix Representation
Maximal Ideal
Module
Monic
Monomial
Monster Group
Negative Definite
Negative Semidefinite
Nilpotent
Noetherian Ring
Noncommutative Ring
Nondegenerate
Nondegenerate Conic
Normal Subgroup
Normalizer
North Pole
Null Space
Null Vector
Octahedral Group
One Parameter Group
Orbit
Orbit Sum
Order
Orientation Preserving
Orientation Reversing
Orthogonal
Orthogonal Basis
Orthogonal Complement
Orthogonal Group
Orthogonal Operator
Orthogonal Projection
Orthogonal Representation
Orthogonal Sum
Orthogonal Vector
Orthonormal Basis
Orthonormal Set
P Group
Partition
Permutation
Permutation Representation
Plane Algebraic Curve
Point Group
Polynomial
Positive Definite
Positive Semidefinite
Prime Field
Prime Ideal
Primitive
Primitive Element
Primitive Root
Principal Ideal
Principal Ideal Domain
Product Group
Product Ideal
Product Ring
Product Set
Projective Group
Proper Divisor
Proper Ideal
Proper Subgroup
Proper Subspace
Quadratic Number Field
Quadric Surface
Quaternion Algebra
Quaternion Group
Quotient Group
Quotient Ring
Ramify
Rational Canonical Form
Reflection
Regular Representation
Relation
Representation
Residue
Resolvent Cubic
Riemann Surface
Right Coset
Ring Extension
Ring Homomorphism
Ring Of Integers
Rotation
Rotation Group
Rotation Matrix
Schur's Lemma
Second Sylow Theorem
Self Adjoint
Shift Operator
Sieve
Sieve Of Eratosthenes
Sign Homomorphism
Simple
Singular Operator
Singular Point
Size Function
Skew Hermitian
Skew Symmetric
Span
Special
Special Linear Group
Special Orthogonal Group
Special Unitary Group
Spin
Spin Group
Spin Homomorphism
Splitting Field
Splitting Theorem
Sporadic Group
Squarefree
Stabilizer
Standard Basis
Standard Hermitian Form
Subdiagonal
Subfield
Subgroup
Subgroup Index
Submodule
Subring
Subspace
Superdiagonal
Sylow P Subgroup
Sylvester's Inertia Law
Sylvester's Signature
Symmetric
Symmetric Functions Theorem
Symmetric Group
Symmetric Operator
Symmetric Polynomial
Symplectic Group
Tetrahedral Group
The Spectral Theorem
Third Sylow Theorem
Total Degree
Trace
Transcendental Number
Translation Group
Transposition
Trivial Homomorphism
Trivial Representation
Trivial Subgroup
Truncated Polyhedron
Tschirnhausen Transformation
Unbranched Covering
Unique Factorization Domain
Unit
Unit Ideal
Unit Sphere
Unitary
Unitary Group
Unitary Matrix
Vector Space
Word
Zero
Zero Divisor
Zero Ideal
... >> Mathematics >> Abstract Algebra >> Group Operation
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Definition: An operation of a group G on a set S is a rule for combining an element g of S and an element s of S to get another element of S. In other words, it is a map GxS -> S.
Source: Algebra, second edition by Michael Artin