On the index conjecture in zero-sum theory: singular case

Abstract

Let $S=(a_1)\cdots (a_k)$ be a minimal zero-sum sequence over a finite cyclic group $G$. The index conjecture states that if $k=4$ and $\gcd (|G|,6)=1$, then $S$ has index $1$. In this paper we prove that if $S$ is singular then the index of $S$ is $1$.

to appear in Int. J. Number Theory; may differ slightly from the final version

References in corpus (2)

• On the index-conjecture of length four minimal zero-sum sequences II
• Minimal zero-sum sequences of length four over finite cyclic groups II

Cited by in corpus (2)

• Improved Bounds for the Index Conjecture in Zero-Sum Theory
• Solution to the index conjecture in zero-sum theory