On the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups

摘要

In an additively written abelian group, a sequence is called zero-sum free if each of its nonempty subsequences has sum different from the zero element of the group. In this paper, we consider the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups . Among which, we determine the structure of the long zero-sum free sequences of length between and , where is an odd integer, and we provide a general description on the structure of n-zero-sum free sequences of length n + l, where and p is the smallest prime dividing n.