Subsequence sums of a zero-sumfree sequence

Let GG be a finite abelian group, and let SS be a sequence of elements in GG. Let f(S)f(S) denote the number of elements in GG which can be expressed as the sum over a nonempty subsequence of SS. In this paper, we show that, if SS contains no zero-sum subsequence and the group generated by all elements of SS is not a cyclic group, then f(S)≥2|S|−1f(S)≥2|S|−1. Moreover, we determine all the sequences SS for which equality holds.