Definition:Normal Subset/Definition 5

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:
 * $\forall x, y \in G: x \circ y \in S \implies y \circ x \in S$

Also see

 * Equivalence of Definitions of Normal Subset