# Definition:Subgroup Action

## Definition

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

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

Let $*: H \times G \to G$ be the operation defined as:

$\forall h \in H, g \in G: h * g := h \circ g$

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

## Also see

• Results about the subgroup action can be found here.