Minimal zero-sum sequences of length four over cyclic group with order n=p^αq^β

2014/01/30 by Limeng Xia, Xia, Li-meng, Caixia Shen +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1401.8021

openalex publication_date 2014/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite cyclic group. Every sequence S over G can be written in the form S=(n₁g)⋅...⋅(n_kg) where g∈ G and n₁,⋯,n_k∈[1,\hbox\rm ord(g)], and the index \ind S of S is defined to be the minimum of (n₁+⋯+n_k)/\hbox\rm ord(g) over all possible g∈ G such that ⟨ g⟩=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.

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