# 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. |