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Finite groups of derangements on the n-cube II

G ) = 2s for some non-negative integer s. The proof of this result is existential but does give some ideas on what n could be. Given k ∈ N and a finite group G, it is shown that G is isomorphic to a subgroup of the group of symmetries of some n-cube in such a way that G acts freely on the set of k-faces, if and only if, gcd(k,

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