Definition:Normal Subgroup/Definition 1

Definition
Let $G$ be a group and let $H \le G$. That is, let $H$ be a subgroup of $G$.

Then the subgroup $H$ is called a normal subgroup of $G$ iff:


 * $\forall g \in G: g H = H g$

where $g H$ and $H g$ are the left and right cosets respectively of $g$ modulo $H$.