Definition:Normal Subset/Definition 6

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:
 * $N_G \left({S}\right) = G$

where $N_G \left({S}\right)$ denotes the normalizer of $S$ in $G$.

Also see

 * Equivalence of Definitions of Normal Subset