\begin{definition}[Definition:Normal Subset/Definition 4]
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}}:
: $\forall g \in G: S \subseteq g \circ S \circ g^{-1}$
or, equivalently:
: $\forall g \in G: S \subseteq g^{-1} \circ S \circ g$
\end{definition}