Simple Group

A simple group is a mathematical group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group.

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

Examples

Cyclic Group:

A cyclic graph is an (always Abelian) abstract group generated by a single element.

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.
Normal Subgroup:	A normal subgroup is a subgroup that is fixed under conjugation by any element.

Classroom Articles on Group Theory

	Abelian Group	Group Theory
	Dihedral Group	Subgroup
	Finite Group	Symmetric Group
	Group Action	Symmetry Group
	Group Representation

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