2017/01/30 by Fabio Enrique Brochero Martínez, Martínez, Fabio Enrique Brochero, Sávio Ribas +1 · 2 citations
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #semigroups and automata theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1701.08788
Let G be a finite group, written multiplicatively. The Davenport constant of G is the smallest positive integer D(G) such that every sequence of G with D(G) elements has a non-empty subsequence with product 1. Let D2n be the Dihedral Group of order 2n and Q4n be the Dicyclic Group of order 4n. J. J. Zhuang and W. Gao (European J. Combin. 26 (2005), 1053-1059) showed that D(D2n) = n+1 and J. Bass (J. Number Theory 126 (2007), 217-236) showed that D(Q4n) = 2n+1. In this paper, we give explicit characterizations of all sequences S of G such that |S| = D(G) - 1 and S is free of subsequences whose product is 1, where G is equal to D2n or Q4n for some n.