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dc.contributor.authorAvelar, Danilo Vilela-
dc.contributor.authorBrochero Martinez, Fabio Enrique-
dc.contributor.authorRibas, Sávio-
dc.date.accessioned2023-08-18T20:44:48Z-
dc.date.available2023-08-18T20:44:48Z-
dc.date.issued2023pt_BR
dc.identifier.citationAVELAR, 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.pt_BR
dc.identifier.issn0022-314X-
dc.identifier.urihttp://www.repositorio.ufop.br/jspui/handle/123456789/17270-
dc.description.abstractFor 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).pt_BR
dc.language.isoen_USpt_BR
dc.rightsrestritopt_BR
dc.subjectZero-sum problempt_BR
dc.subjectSmall davenport constantpt_BR
dc.subjectGao constantpt_BR
dc.subjectMetacyclic groupspt_BR
dc.titleA note on Bass’ conjecture.pt_BR
dc.typeArtigo publicado em periodicopt_BR
dc.identifier.uri2https://www.sciencedirect.com/science/article/pii/S0022314X23000616pt_BR
dc.identifier.doihttps://doi.org/10.1016/j.jnt.2023.02.014pt_BR
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