Extremal product-one free sequences in Dihedral and Dicyclic Groups |
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Authors: | FE Brochero Martínez Sávio Ribas |
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Institution: | 1. Departamento de Matemática, Universidade Federal de Minas Gerais, UFMG, Belo Horizonte, MG, 30123-970, Brazil;2. Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, IFMG-Campus Avançado Piumhi, Piumhi, MG, 37925-000, Brazil |
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Abstract: | Let be a finite group, written multiplicatively. The Davenport constant of is the smallest positive integer such that every sequence of with elements has a non-empty subsequence with product . Let be the Dihedral Group of order and be the Dicyclic Group of order . Zhuang and Gao (2005) showed that and Bass (2007) showed that . In this paper, we give explicit characterizations of all sequences of such that and is free of subsequences whose product is 1, where is equal to or for some . |
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Keywords: | Zero-sum problem Davenport constant Inverse zero-sum |
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