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2.5: Group Actions
https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Introduction_to_Groups_and_Geometries_(Lyons)/02%3A_Groups/2.05%3A_Group_actions
Show that the orbits of this action of $H$ on $G$ are the same as the cosets of $H\text{.}$ This shows that the two potentially different meanings of $G/H$ (one is the set of cosets, the other...Show that the orbits of this action of $H$ on $G$ are the same as the cosets of $H\text{.}$ This shows that the two potentially different meanings of $G/H$ (one is the set of cosets, the other is the set of orbits of the action of $H$ on $G$ via $R$ ), are in fact in agreement.

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