Minimal zero sum sequences of length four over finite cyclic groups

TextLet G be a finite cyclic group. Every sequence S over G   can be written in the form S=(n1g)⋅…⋅(nlg)S=(n1g)⋅…⋅(nlg) where g∈Gg∈G and n1,…,nl∈[1,ord(g)]n1,…,nl∈[1,ord(g)], and the index ind(S)ind(S) of S   is defined to be the minimum of (n1+⋯+nl)/ord(g)(n1+⋯+nl)/ord(g) over all possible g∈Gg∈G such that 〈g〉=〈supp(S)〉〈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)=1gcd(|G|,6)=1, then every minimal zero-sum sequence of length 4 has index 1.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=BC7josX_xVs.