Definition:Subgroup Action

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

Let $\struct {H, \circ}$ be a subgroup of $G$.

Let $H$ act on $G$ by the rule:
 * $\forall h \in H, g \in G: h * g := h \circ g$

This is the subgroup action of $H$ on $G$.

Also see

 * Subgroup Action is Group Action