Question: Let X be a G-set and let S X. If G s S for all s S, then S is a sub-G-set.

Let X be a G-set and let S ⊆ X. If Gs  ⊆ S for all s ∈ S, then S is a sub-G-set. Characterize a sub-G-set of a G-set X in terms of orbits in X and G.

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