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Let $G$ be a finite cyclic group. Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(n_1g)cdotldotscdot(n_lg)$ where $gin G$ and $n_1, ldots, n_lin[1, ord(g)]$, and the index $ind(S)$ of $S$ is defined to be the minimum of $(n_1+cdots+n_l)/ord(g)$ over all possible $gin G$ such that $langle g rangle =G$. In this paper, we determine the index of any minimal zero-sum sequence $S$ of length 5 when $G=langle grangle$ is a cyclic group of a prime order and $S$ has the form $S=g^2(n_2g)(n_3g)(n_4g)$. It is shown that if $G=langle grangle$ is a cyclic group of prime order $p geq 31$, then every minimal zero-sum sequence $S$ of the above mentioned form has index 1 except in the case that $S=g^2(frac{p-1}{2}g)(frac{p+3}{2}g)((p-3)g)$.
Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)cdotldotscdot(n_lg)$ where $gin G$ and $n_1, ldots, n_lin[1, ord(g)]$, and the index $ind(S)$ of $S$ is defined to be the minimum of $(n_1+cdots+n_l)/or
Let $p > 155$ be a prime and let $G$ be a cyclic group of order $p$. Let $S$ be a minimal zero-sum sequence with elements over $G$, i.e., the sum of elements in $S$ is zero, but no proper nontrivial subsequence of $S$ has sum zero. We call $S$ is uns
Let $G$ be a finite cyclic group. Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(x_1g)cdotldotscdot(x_lg)$ where $gin G$ and $x_1, ldots, x_lin[1, ord(g)]$, and the index $ind(S)$ of $S$ is defined to be the minimum of $(x_1
Let $mathcal{S}$ be a finite cyclic semigroup written additively. An element $e$ of $mathcal{S}$ is said to be idempotent if $e+e=e$. A sequence $T$ over $mathcal{S}$ is called {sl idempotent-sum free} provided that no idempotent of $mathcal{S}$ can
We study the maximal cross number $mathsf{K}(G)$ of a minimal zero-sum sequence and the maximal cross number $mathsf{k}(G)$ of a zero-sum free sequence over a finite abelian group $G$, defined by Krause and Zahlten. In the first part of this paper, w