# Definition:Subset Product Action

## Definition

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

Let $\HH$ be the set of subgroups of $G$.

### Left Subset Product Action

The (left) subset product action of $G$ is the group action $*: G \times \powerset G \to \powerset G$:

$\forall g \in G, S \in \powerset G: g * S = g \circ S$

### Right Subset Product Action

The (right) subset product action of $G$ is the group action $*: G \times \powerset G \to \powerset G$:

$\forall g \in G, S \in \powerset G: g * S = S \circ g$

## Also see

• Results about the Subset Product action can be found here.