English

Extremal product-one free sequences in $C_q \rtimes_s C_m$

Number Theory 2017-02-01 v1

Abstract

Let GG be a finite group, written multiplicatively. The Davenport constant of GG is the smallest positive integer dd such that every sequence of GG with dd elements has a non-empty subsequence with product 11. Let CnZnC_n \simeq \mathbb Z_n be the cyclic group of order nn. Bass (2007) showed that the Davenport constant of the metacyclic group CqsCmC_q \rtimes_s C_m, where qq is a prime number and ordq(s)=m2\text{ord}_q(s) = m \ge 2, is m+q1m+q-1. In this paper, we explicit the form of all sequences SS of CqsCmC_q \rtimes_s C_m, with q+m2q+m-2 elements, that are free of product-11 subsequences.

Keywords

Cite

@article{arxiv.1610.09870,
  title  = {Extremal product-one free sequences in $C_q \rtimes_s C_m$},
  author = {Fabio Enrique Brochero Martínez and Sávio Ribas},
  journal= {arXiv preprint arXiv:1610.09870},
  year   = {2017}
}