\begin{definition}[Definition:Normal Subgroup/Definition 2]
Let $G$ be a group.
Let $N$ be a subgroup of $G$.
$N$ is a '''normal subgroup of $G$''' {{iff}}:
: Every right coset of $N$ in $G$ is a left coset
that is:
: The right coset space of $N$ in $G$ equals its left coset space.
\end{definition}