Free actions of abelian p-groups on the n-Torus

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dc.contributor.authorGonçalves, Daciberg Lima
dc.contributor.authorVieira, João Peres [UNESP]
dc.contributor.institutionUniversidade de São Paulo (USP)
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.date.accessioned2022-04-28T19:56:58Z
dc.date.available2022-04-28T19:56:58Z
dc.date.issued2005-01-01
dc.description.abstractIn this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus Tn. Set H ≅ ℤpk1 h1 × ℤpk2h2 × ⋯ × ℤpkrhr, r ≥ 1, k1 ≥ k2 ≥ ⋯ ≥ kr ≥ 1, p prime. Suppose that the group H acts freely on Tn and the induced representation on π 1(Tn) ≅ ℤn is faithful and has first Betti number b. We show that the numbers n, p, b, ki and h i (i = 1, ⋯ , r) satisfy some relation. In particular, when H ≅ ℤph, the minimum value of n is φ(p) + b when b ≥ 1. Also when H ≅ ℤpk1, × ℤp the minimum value of n is φ(pk1)+ p - 1 + 6 for 6 ≥ 1. Here φ denotes the Euler function. © 2005 University of Houston.en
dc.description.affiliationDepartamento de Matemática IME USP, Caixa Postal 66.281, CEP 05311-970, São Paulo - SP
dc.description.affiliationDepartamento de Matemática IGCE UNESP, Caixa Postal 178, CEP 13500-230, Rio Claro - SP
dc.description.affiliationUnespDepartamento de Matemática IGCE UNESP, Caixa Postal 178, CEP 13500-230, Rio Claro - SP
dc.format.extent87-102
dc.identifier.citationHouston Journal of Mathematics, v. 31, n. 1, p. 87-102, 2005.
dc.identifier.issn0362-1588
dc.identifier.scopus2-s2.0-17244380104
dc.identifier.urihttp://hdl.handle.net/11449/224509
dc.language.isoeng
dc.relation.ispartofHouston Journal of Mathematics
dc.sourceScopus
dc.subjectBieberbach groups
dc.subjectFree actions
dc.subjectIntegral representation
dc.subjectp-groups
dc.titleFree actions of abelian p-groups on the n-Torusen
dc.typeArtigo

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