Minimal zero sum sequences of length four over finite cyclic groups

Text. Let G be a finite cyclic group. Every sequence S over G can be written in the form S = (n(1)g) "... " (n(1)g) where g is an element of G and n(1) ,..., n(1) is an element of [1, ord(g)], and the index ind(S) of S is defined to be the minimum of (n(1) + ... + n(1))/ord(g) over all possible g is an element of G such that (g) = (supp(S)). The problem regarding the index of sequences has been studied in a series of papers, and a main focus is to determine sequences of index 1. In the present paper, we show that if G is a cyclic of prime power order such that gcd([G], 6) = 1, then every minimal zero-sum sequence of length 4 has index 1. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=BC7josX_xVs. (C) 2010 Elsevier Inc. All rights reserved.