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