Group Action

A group action is the association of each of a mathematical group's elements with a permutation of the elements of a set.

Group action is a college-level concept that would be first encountered in an abstract algebra course covering group theory.

Examples

Group Representation:

A group representation is a mathematical group action on a vector space.

Prerequisites

Group:

A mathematical group is a set of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property.

Classroom Articles on Group Theory

	Abelian Group	Normal Subgroup
	Cyclic Group	Simple Group
	Dihedral Group	Subgroup
	Finite Group	Symmetric Group
	Group Theory	Symmetry Group

Classroom Articles on Abstract Algebra (Up to College Level)

	Abstract Algebra	Gaussian Integer
	Algebra	Ideal
	Algebraic Number	Isomorphism
	Boolean Algebra	Quaternion
	Field	Ring
	Finite Field