A note on Bass’ conjecture.
dc.contributor.author | Avelar, Danilo Vilela | |
dc.contributor.author | Brochero Martinez, Fabio Enrique | |
dc.contributor.author | Ribas, Sávio | |
dc.date.accessioned | 2023-08-18T20:44:48Z | |
dc.date.available | 2023-08-18T20:44:48Z | |
dc.date.issued | 2023 | pt_BR |
dc.description.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). | pt_BR |
dc.identifier.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: <https://www.sciencedirect.com/science/article/pii/S0022314X23000616>. Acesso em: 06 jul. 2023. | pt_BR |
dc.identifier.doi | https://doi.org/10.1016/j.jnt.2023.02.014 | pt_BR |
dc.identifier.issn | 0022-314X | |
dc.identifier.uri | http://www.repositorio.ufop.br/jspui/handle/123456789/17270 | |
dc.identifier.uri2 | https://www.sciencedirect.com/science/article/pii/S0022314X23000616 | pt_BR |
dc.language.iso | en_US | pt_BR |
dc.rights | restrito | pt_BR |
dc.subject | Zero-sum problem | pt_BR |
dc.subject | Small davenport constant | pt_BR |
dc.subject | Gao constant | pt_BR |
dc.subject | Metacyclic groups | pt_BR |
dc.title | A note on Bass’ conjecture. | pt_BR |
dc.type | Artigo publicado em periodico | pt_BR |
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