Minimal zero-sum sequences of length four over cyclic group with order n = p(alpha)q(beta)

作者：Xia Li meng^*; Shen Caixia

来源：Journal of Number Theory, 2013, 133(12): 4047-4068.

DOI：10.1016/j.jnt.2013.06.008

• Minimal zero-sum sequence
• Cyclic groups
• Index of sequences

Let G be a finite cyclic group. Every sequence S over G can be written in the form S = (n(1)g).....(n(k)g) where g is an element of G and n(1), ..., n(k) is an element of [1, ord(g)], and the index ind S of S is defined to be the minimum of (n(1) +...+ n(k))/ord(g) over all possible g is an element of G such that < g > = G. A conjecture says that if G is finite such that gcd(vertical bar G vertical bar, 6) = 1, then id(S) = 1 for every minimal zero-sum sequence S. In this paper, we prove that the conjecture holds if vertical bar G vertical bar has two prime factors.

• 出版日期2013-12
• 单位江苏大学