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Minimal zero-sum sequences of length four over cyclic group with order $n=p^\alpha q^\beta$
- Publication Year :
- 2014
-
Abstract
- Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot...\cdot(n_kg)$ where $g\in G$ and $n_1,\cdots,n_k\in[1,{\hbox{\rm ord}}(g)]$, and the index $\ind S$ of $S$ is defined to be the minimum of $(n_1+\cdots+n_k)/\hbox{\rm ord}(g)$ over all possible $g\in G$ such that $\langle g\rangle=G$. A conjecture says that if $G$ is finite such that $\gcd(|G|,6)=1$, then $\ind(S)=1$ for every minimal zero-sum sequence $S$. In this paper, we prove that the conjecture holds if $|G|$ has two prime factors.<br />Comment: Journal of Number Theory (2013). arXiv admin note: text overlap with arXiv:1303.1682, arXiv:1303.1676, arXiv:1401.7981, arXiv:1401.7979
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1401.8021
- Document Type :
- Working Paper