Strong conciseness of coprime commutators in profinite groups

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorHeinrich-Heine-Universität, Mathematisches Institut-
Autor(es): dc.contributorEuskal Herriko Unibertsitatea UPV/EHU, Department of Mathematics-
Autor(es): dc.contributorUniversity of Brasilia, Department of Mathematics-
Autor(es): dc.creatorHeras, Iker de las-
Autor(es): dc.creatorPintonello, Matteo-
Autor(es): dc.creatorShumyatsky, Pavel-
Data de aceite: dc.date.accessioned2024-10-23T15:02:47Z-
Data de disponibilização: dc.date.available2024-10-23T15:02:47Z-
Data de envio: dc.date.issued2024-04-12-
Data de envio: dc.date.issued2024-04-12-
Data de envio: dc.date.issued2022-
Fonte completa do material: dc.identifierhttp://repositorio2.unb.br/jspui/handle/10482/48072-
Fonte completa do material: dc.identifierhttps://doi.org/10.1016/j.jalgebra.2023.06.003-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/872892-
Descrição: dc.descriptionLet G be a profinite group. The coprime commutators γ∗ j and δ∗ j are defined as follows. Every element of G is both a γ∗ 1 -value and a δ∗ 0 -value. For j ≥ 2, let X be the set of all elements of G that are powers of γ∗ j−1-values. An element a is a γ∗ j -value if there exist x ∈ X and g ∈ G such that a = [x, g] and (|x|, |g|) = 1. For j ≥ 1, let Y be the set of all elements of G that are powers of δ∗ j−1-values. The element a is a δ∗ j -value if there exist x, y ∈ Y such that a = [x, y] and (|x|, |y|) = 1. In this paper we establish the following results. A profinite group G is finite-by-pronilpotent if and only if there is k such that the set of γ∗ k-values in G has cardinality less than 2ℵ0 (Theorem 1.1). A profinite group G is finite-by-(prosoluble of Fitting height at most k) if and only if there is k such that the set of δ∗ k-values in G has cardinality less than 2ℵ0 (Theorem 1.2).-
Descrição: dc.descriptionInstituto de Ciências Exatas (IE)-
Descrição: dc.descriptionDepartamento de Matemática (IE MAT)-
Idioma: dc.languageen-
Publicador: dc.publisherElsevier Inc.-
Relação: dc.relationhttps://www.sciencedirect.com/science/article/pii/S002186932300282X?via%3Dihub#kws0020-
Direitos: dc.rightsAcesso Restrito-
Palavras-chave: dc.subjectGrupos profinitos-
Palavras-chave: dc.subjectComutadores-
Título: dc.titleStrong conciseness of coprime commutators in profinite groups-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional – UNB

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