Extremal product-one free sequences in Cq s Cm.

Abstract

Let G be a finite group. The Davenport constant of G is the smallest positive integer d such that every sequence over G with d elements has a non-empty subsequence with product 1. Let Cn be the cyclic group of order n. Bass [1] showed that the Davenport constant of the metacyclic group Cq s Cm, where q is a prime number and ordq(s) = m ≥ 2, is m+ q − 1. In this paper, we determine the form of all sequences S of Cq s Cm, with q + m − 2 elements that are product-one free.