Normal Subgroup

definitiongroup-theory

Definition

A normal subgroup $N⊴G$, is a subgroup $N\le G$ such that $N$ is closed under conjugation by any element $g\in G$.

Additionally, a normal subgroup $N⊴G$ is a subgroup such that the cosets of $N$, $gN$ or $Ng$ for all $g\in G$, form a group.

Examples