# Normal Subgroup

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

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

### 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. |

Subgroup: | A subgroup is a subset of a mathematical group that is also a group. |