\begin{definition}[Definition:Normal Subgroup/Definition 3]
Let $G$ be a group.
Let $N$ be a subgroup of $G$.
$N$ is a '''normal subgroup of $G$''' {{iff}}:
:$\forall g \in G: g \circ N \circ g^{-1} \subseteq N$
:$\forall g \in G: g^{-1} \circ N \circ g \subseteq N$
where $g \circ N$ etc. denotes the subset product of $g$ with $N$.
\end{definition}