\begin{definition}[Definition:Normal Subset/Definition 3]
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}}:
: $\forall g \in G: g \circ S \circ g^{-1} \subseteq S$
or, equivalently:
: $\forall g \in G: g^{-1} \circ S \circ g \subseteq S$
\end{definition}