Inverse problems associated with subsequence sums in {{\displaystyle G}}_p\oplus {{\displaystyle C}}_p

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 \left|{{\displaystyle S}}_H\right|\le \left|H\right|-\mathrm{1} holds for every proper subgroup H of G; where S_H 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 \mathrm{0}\notin {\displaystyle \sum (S)}0; where {\displaystyle \sum (S)}\subset 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 {\displaystyle \sum (S)} when S is a regular sequence or a zero-sum free sequence over G={{\displaystyle G}}_p\oplus {{\displaystyle C}}_p, where p is a prime.

Key words： Inverse problems; subsequence sums; regular sequences; zero-sum free sequences

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