Avelar, Danilo VilelaBrochero Martinez, Fabio EnriqueRibas, Sávio2023-08-182023-08-182023AVELAR, 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: <https://www.sciencedirect.com/science/article/pii/S0022314X23000616>. Acesso em: 06 jul. 2023.0022-314Xhttp://www.repositorio.ufop.br/jspui/handle/123456789/17270For 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).en-USrestritoZero-sum problemSmall davenport constantGao constantMetacyclic groupsArtigo publicado em periodicohttps://www.sciencedirect.com/science/article/pii/S0022314X23000616https://doi.org/10.1016/j.jnt.2023.02.014