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A permutation group G acting on a set Ω induces a permutation group on the set of all subsets 𝒫(Ω). Let G be a finite permutation group of degree n, and let s(G) denote the number of set-orbits of G. We determine over all solvable groups G. This answers a question of Babai and Pyber [Citation1].
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I would like to thank the referee for the valuable suggestions.
Communicated by J. Zhang.
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