Definition:Normal Subset/Definition 7

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:

$\forall g \in G: g \circ S \subseteq S \circ g$

or:

$\forall g \in G: S \circ g \subseteq g \circ S$

Also see

• Equivalence of Definitions of Normal Subset