Definition:Subset Product Action/Right
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Definition
Let $\struct {G, \circ}$ be a group.
Let $\powerset G$ be the power set of $G$.
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.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 5.5$. Groups acting on sets: Example $104$