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Title: A note on Bass’ conjecture.
Authors: Avelar, Danilo Vilela
Brochero Martinez, Fabio Enrique
Ribas, Sávio
Keywords: Zero-sum problem
Small davenport constant
Gao constant
Metacyclic groups
Issue Date: 2023
Citation: AVELAR, D. V.; BROCHERO MARTINEZ, F. E.; RIBAS, S. A note on Bass’ conjecture. Journal of Number Theory, v. 249, p. 462–469, 2023. Disponível em: <>. Acesso em: 06 jul. 2023.
Abstract: For a finite group G, we denote by d(G) and by E(G), respectively, the small Davenport constant and the Gao constant of G. Let Cn be the cyclic group of order n and let Gm,n,s = Cn s Cm be a metacyclic group. In [2, Conjecture 17], Bass conjectured that d(Gm,n,s) = m + n − 2 and E(Gm,n,s) = mn + m + n − 2 provided ordn(s) = m. In this paper, we show that the assumption ordn(s) = m is essential and cannot be removed. Moreover, if we suppose that Bass’ conjecture holds for Gm,n,s and the mn-product-one free sequences of maximal length are well behaved, then Bass conjecture also holds for G2m,2n,r, where r2 ≡ s (mod n).
ISSN: 0022-314X
Appears in Collections:DEMAT - Artigos publicados em periódicos

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