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.