Definition:Normal Subset/Definition 2

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

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