# Definition:Normal Subset/Definition 6

## Definition

Let $\struct {G, \circ}$ be a group.

Let $S \subseteq G$ be a general subset of $G$.

Then $S$ is a normal subset of $G$ if and only if:

$\map {N_G} S = G$

where $\map {N_G} S$ denotes the normalizer of $S$ in $G$.