Definition:Subset Product Action

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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.