Definition:Normal Subgroup/Definition 2

Definition
Let $\left({G, \circ}\right)$ be a group whose identity is $e$.

Let $N$ be a subgroup of $G$.

Then $N$ is normal in $G$ iff:
 * Every right coset of $N$ in $G$ is a left coset.

Equivalently:
 * The right coset space of $N$ in $G$ equals its left coset space.