http://repositorio.unb.br/handle/10482/44909
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 |
Aparece nas coleções: | Artigos publicados em periódicos e afins |
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