Título:	Centralizers of commutators in finite groups
Autor(es):	Detomi, Eloisa Morigi, Marta Shumyatsky, Pavel
E-mail do autor:	mailto:eloisa.detomi@unipd.it mailto:marta.morigi@unibo.it mailto:pavel@unb.br
Assunto:	Comutadores Centralizadores Conjugação
Data de publicação:	2022
Editora:	Elsevier
Referência:	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.
Abstract:	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.
DOI:	https://doi.org/10.1016/j.jalgebra.2022.09.005
Versão da editora:	https://www.sciencedirect.com/science/article/pii/S0021869322004318?via%3Dihub
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