Definition:Normal Subset/Definition 4

Definition
Let $\left({G,\circ}\right)$ be a group and let $N \subseteq G$.

Then $N$ is a normal subset of $G$ iff:
 * $\forall g \in G: N \subseteq g \circ N \circ g^{-1}$ or, equivalently,
 * $\forall g \in G: N \subseteq g^{-1} \circ N \circ g$