Definition:Normal Subset/Definition 3
Jump to navigation
Jump to search
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:
- $\forall g \in G: g \circ S \circ g^{-1} \subseteq S$
or, equivalently:
- $\forall g \in G: g^{-1} \circ S \circ g \subseteq S$