Definition:Normal Subset/Definition 4

Definition
Let $\left({G, \circ}\right)$ 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:
 * $\forall g \in G: S \subseteq g^{-1} \circ S \circ g$

Also see

 * Equivalence of Definitions of Normal Subset