2021/07/16 by Martínez, Fabio Enrique Brochero, Ribas, Sávio
#11B50 #11P70 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2108.00822
Let G be a finite group multiplicatively written. The small Davenport constant of G is the maximum positive integer \sf d(G) such that there exists a sequence S of length \sf d(G) for which every subsequence of S is product-one free. Let s2 ≡ 1 \pmod n, where s \not≡ ±1 \pmod n. It has been proven that \sf d(Cn \rtimess C2) = n (see Lemma 6 of [Zhuang, Gao; Europ. J. Combin. 26 (2005), 1053-1059]). In this paper, we determine all sequences over Cn \rtimess 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 \rtimess C2, including the quasidihedral groups and the modular maximal-cyclic groups.