\begin{definition}[Definition:Normal Subset/Definition 6]
Let $\struct {G, \circ}$ be a group.
Let $S \subseteq G$ be a general subset of $G$.
Then $S$ is a '''normal subset of $G$''' {{iff}}:
:$\map {N_G} S = G$
where $\map {N_G} S$ denotes the normalizer of $S$ in $G$.
\end{definition}