Strong conciseness of coprime commutators in profinite groups

Heras, Iker de las; Pintonello, Matteo; Shumyatsky, Pavel

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Campo DC	Valor	Lengua/Idioma
dc.contributor.author	Heras, Iker de las	-
dc.contributor.author	Pintonello, Matteo	-
dc.contributor.author	Shumyatsky, Pavel	-
dc.date.accessioned	2024-04-12T11:09:05Z	-
dc.date.available	2024-04-12T11:09:05Z	-
dc.date.issued	2023	-
dc.identifier.citation	HERAS, Iker de las; PINTONELLO, Matteo; SHUMYATSKY, Pavel. Strong conciseness of coprime commutators in profinite groups. Journal of Algebra, [S. l.], v. 633, p. 1-19, 1 November 2023. DOI: https://doi.org/10.1016/j.jalgebra.2023.06.003.	pt_BR
dc.identifier.uri	http://repositorio.unb.br/handle/10482/48072	-
dc.language.iso	eng	pt_BR
dc.publisher	Elsevier Inc.	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Strong conciseness of coprime commutators in profinite groups	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Grupos profinitos	pt_BR
dc.subject.keyword	Comutadores	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.jalgebra.2023.06.003	pt_BR
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S002186932300282X?via%3Dihub#kws0020	pt_BR
dc.description.abstract1	Let 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).	pt_BR
dc.contributor.affiliation	Heinrich-Heine-Universität, Mathematisches Institut	pt_BR
dc.contributor.affiliation	Euskal Herriko Unibertsitatea UPV/EHU, Department of Mathematics	pt_BR
dc.contributor.affiliation	University of Brasilia, Department of Mathematics	pt_BR
dc.description.unidade	Instituto de Ciências Exatas (IE)	pt_BR
dc.description.unidade	Departamento de Matemática (IE MAT)	pt_BR
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