Inverse problems associated with subsequence sums in Cp ⊕ Cp

Abstract

Let G be a finite abelian group and S be a sequence with elements of G. We say that S is a regular sequence over G if ∣SH∣ ⩽ ∣H∣ − 1 holds for every proper subgroup H of G, where SH denotes the subsequence of S consisting of all terms of S contained in H. We say that S is a zero-sum free sequence over G if 0 ∉ Ω(S), where Ω(S) ⊂ G denotes the set of group elements which can be expressed as a sum of a nonempty subsequence of S. In this paper, we study the inverse problems associated with Ω(S) when S is a regular sequence or a zero-sum free sequence over G = Cp ⊕ Cp, where p is a prime.