\begin{definition}[Definition:Normal Subset/Definition 1]
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}}:
:$\forall g \in G: g \circ S = S \circ g$
\end{definition}