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Published online by Cambridge University Press: 01 March 1998
Let S be a generating subset of a cyclic group G such that 0=∉S and [mid ]S[mid ][ges ]5. We show that the number of sums of the subsets of S is at least min([mid ]G[mid ], 2[mid ]S[mid ]). Our bound is best possible. We obtain similar results for abelian groups and mention the generalization to nonabelian groups.