Subsequence sums of a zero-sumfree sequence

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