ASL STEM

Commutator Sign Video

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Definition

The commutator aba^(-1)b^(-1) is an element associated to a pair a, b of elements of a group.

Source: Algebra, second edition by Michael Artin

Example

Two elements a and b of a group commute, ab=ba, if and only aba^(-1)=b, and this is true if and only if aba^(-1)b^(-1)=1.

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> Mathematics

> Abstract Algebra

> Commutator

+ General Linear Group *

+ Induced Law *

+ Isomorphic *

+ Lagrange's Theorem *

+ Special Linear Group *

+ Proper Subgroup *

+ Law Of Composition *

+ Trivial Homomorphism *

+ Inclusion Map *

+ Sign Homomorphism *

+ Alternating Group *

+ Normal Subgroup

+ Isomorphism

+ Left Coset *

+ Isomorphism Class *

- Commutator *

+ Correspondence Theorem *

+ Counting Formula *

+ Stabilizer *

+ Conjugate Subgroup *

+ Permutation Representation *

+ Commutator Subgroup *

+ Equator *

+ Fixed Vector *

+ First Isomorphism Theorem *

+ Proper Subspace *

+ Prime Field *

+ Characteristic Zero *

+ Basechange Matrix *

+ Direct Sum *

+ Dimension Formula *

+ Jordan Canonical Form *

+ Jordan Decomposition Theorem *

+ Nilpotent *

+ Kronecker Delta *

+ Orthogonal Group *

+ Special Orthogonal Group *

+ Orthogonal Operator *

+ Cayley Hamilton Theorem *

+ Matrix Exponential *

+ Unitary Matrix *

+ First Sylow Theorem *

+ Translation Group *

+ Discrete Subgroup *

+ Representation *

+ Lattice *

+ Point Group *

+ Tetrahedral Group *

+ Octahedral Group *

+ Icosahedral Group *

+ Truncated Polyhedron *

+ Sylow P Subgroup *

+ Second Sylow Theorem *

+ Third Sylow Theorem *

+ Bilinear Form *

+ Positive Definite *

+ Negative Semidefinite *

+ Negative Definite *

+ Indefinite *

+ Hermitian Form *

+ Standard Hermitian Form *

+ Hermitian Symmetry *

+ Associates *

+ Positive Semidefinite *

+ Nondegenerate *

+ Degenerate *

+ Orthogonal Sum *

+ Orthogonal Projection *

+ Hermitian Space *

+ Adjoint Operator *

+ Symmetric Operator *

+ Degenerate Conic *

+ Conics *

+ Nondegenerate Conic *

+ Orthogonal Vector *

+ Quadric Surface *

+ Symplectic Group *

+ Lorentz Group *

+ Lorentz Transformations *

+ Special *

+ Special Unitary Group *

+ Quaternion Algebra *

+ Skew Hermitian *

+ Spin Homomorphism *

+ Orthogonal Representation *

+ Spin Group *

+ Longitude *

+ Maschke's Theorem *

+ One Parameter Group *

+ Gaussian Integers *

+ Bracket *

+ Jacobi Identity *

+ Lie Algebra *

+ Irreducible Character *

+ Complex Algebraic Group *

+ Exceptional Groups *

+ Lie Type *

+ Sporadic Group *

+ Matrix Representation *

+ Trivial Representation *

+ Group Character *

+ Mathieu Group *

+ Monster Group *

+ Regular Representation *

+ Proper Divisor *

+ Compact Group *

+ Noncommutative Ring *

+ Leading Coefficient *

+ Monic *

+ Total Degree *

+ Homogeneous Polynomial *

+ Subring

+ Ring Homomorphism *

+ Hilbert's Nullstellensatz *

+ Zero *

+ Common Zeros *

+ Algebraic Variety *

+ Bezout Bound *

+ Riemann Surface *

+ Plane Algebraic Curve *

+ Cyclotomic Polynomial *

+ Branched Covering *

+ Unbranched Covering *

+ Branch Points *

+ Size Function *

+ Euclidean Domain *

+ Principal Ideal Domain *

+ Irreducible Factorization *

+ Unique Factorization Domain *

+ Gauss's Lemma *

+ Sieve *

+ Sieve Of Eratosthenes *

+ Eisenstein Criterion *

+ Gaussian Prime *

+ Algebraic Integer *

+ Quadratic Number Field *

+ Invertible Integer Matrix *

+ Elementary Integer Matrix *

+ Complete Set *

+ Cusp *

+ Irreducible Representation *

+ Quotient Ring *

+ Ascending Chain Condition *

+ Noetherian Ring *

+ Hilbert Basis Theorem *

+ Rational Canonical Form *

+ Extension Field *

+ Algebraic Number Field *

+ Finite Field *

+ Function Field *

+ Finite Extension *

+ Primitive Element *

+ Algebraically Closed *

+ Symmetric Polynomial *

+ Sylvester's Inertia Law *

+ Sylvester's Signature *

+ Projective Group *

+ Orbit Sum *

+ Elementary Symmetric Functions *

+ Symmetric Functions Theorem *

+ Discriminant *

+ Tschirnhausen Transformation *

+ Splitting Field *

+ Splitting Theorem *

+ Galois Group *

+ Galois Extension Field *

+ Fixed Field *

+ Fixed Field Theorem *

+ Luroth's Theorem *

+ Intermediate Field *

+ Crystallographic Point Group *

+ Free Semigroup *

+ Resolvent Cubic *

+ Cyclotomic Field *

+ Kronecker Weber Theorem *

+ Kummer Extension *

+ Linear Operator *

+ Invertible Operator *

+ Singular Operator *

+ Generalized Eigenvector *

+ Schur's Lemma *

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