Definition:Subgroup Action

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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.