On minimal zero-sum sequences of length four over cyclic groups

Abstract

Let $G$ be a cyclic group of order $n$. It has been conjectured that if $\operatorname{gcd}(n,6)=1$, then every minimal zero-sum sequence $S$ of length $4$ over $G$ has index $1$, that is, $S=(n_1g)\cdot (n_2g)\cdot (n_3g)\cdot (n_4g)$ for some gener