Centralizers of commutators in finite groups

Detomi, Eloisa; Morigi, Marta; Shumyatsky, Pavel

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Campo DC	Valor	Lengua/Idioma
dc.contributor.author	Detomi, Eloisa	-
dc.contributor.author	Morigi, Marta	-
dc.contributor.author	Shumyatsky, Pavel	-
dc.date.accessioned	2022-09-26T19:37:01Z	-
dc.date.available	2022-09-26T19:37:01Z	-
dc.date.issued	2022	-
dc.identifier.citation	DETOMI, Eloisa; MORIGI, Marta; SHUMYATSKY, Pavel. Centralizers of commutators in finite groups. Journal of Algebra, v. 612, n. 15, p. 475-486, dez. 2022. DOI 10.1016/j.jalgebra.2022.09.005. Disponível em: https://www.sciencedirect.com/science/article/pii/S0021869322004318?via%3Dihub. Acesso em: 26 set. 2022.	pt_BR
dc.identifier.uri	https://repositorio.unb.br/handle/10482/44909	-
dc.language.iso	Inglês	pt_BR
dc.publisher	Elsevier	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Centralizers of commutators in finite groups	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Comutadores	pt_BR
dc.subject.keyword	Centralizadores	pt_BR
dc.subject.keyword	Conjugação	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.jalgebra.2022.09.005	pt_BR
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0021869322004318?via%3Dihub	pt_BR
dc.description.abstract1	Let G be a finite group. A coprime commutator in G is any element that can be written as a commutator [x, y] for suitable x, y ∈ G such that π(x) ∩ π(y) = ∅. Here π(g) denotes the set of prime divisors of the order of the element g ∈ G. An anticoprime commutator is an element that can be written as a commutator [x, y], where π(x) = π(y). The main results of the paper are as follows. If \|xG\| ≤ n whenever x is a coprime commutator, then G has a nilpotent subgroup of n-bounded index. If \|xG\| ≤ n for every anti-coprime commutator x ∈ G, then G has a subgroup H of nilpotency class at most 4 such that [G : H] and \|γ4(H)\| are both n-bounded. We also consider finite groups in which the centralizers of coprime, or anti-coprime, commutators are of bounded order.	pt_BR
dc.contributor.email	mailto:eloisa.detomi@unipd.it	pt_BR
dc.contributor.email	mailto:marta.morigi@unibo.it	pt_BR
dc.contributor.email	mailto:pavel@unb.br	pt_BR
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