Extremal product-one free sequences over Cn s C2.

Abstract

Let G be a finite group multiplicatively written. The small Davenport constant of G is the maximum positive integer d(G) such that there exists a product-one free sequence S of length d(G). Let s2 ≡ 1 (mod n), where s ≡ ±1 (mod n). It has been proven that d(Cn s C2) = n (see [13, Lemma 6]). In this paper, we determine all sequences over Cn s C2 of length n which are product-one free. It completes the classification of all product-one free sequences over every group of the form Cn s C2, including the quasidihedral groups and the modular maximal-cyclic groups.