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(modn), where s≢±1(modn). It has been proven that d(Cn⋊sC2)=n (see [13, Lemma 6]). In this paper, we determine all sequences over Cn⋊sC2 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⋊sC2, including the quasidihedral groups and the modular maximal-cyclic groups.
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