Título:	Nilpotent residual of a finite group
Autor(es):	Rodrigues, Eliana Melo, Emerson Ferreira de Ercan, Gülin
ORCID:	https://orcid.org/0000-0001-7222-663X https://orcid.org/0000-0003-1476-5314
Afiliação do autor:	Instituto Federal de Goiás, Department of Academic Areas University of Brasilia, Department of Mathematics Middle East Technical University, Department of Mathematics
Assunto:	Automorfismos Grupo de Frobenius Grupo finito
Data de publicação:	17-Nov-2023
Editora:	Elsevier
Referência:	RODRIGUES, Eliana; MELO, Emerson Ferreira de; ERCAN, Gülin. Nilpotent residual of a finite group. Journal of Algebra, [S.l.], v. 641, p. 534-545, 2024. DOI: https://doi.org/10.1016/j.jalgebra.2023.11.011. Disponível em: https://www.sciencedirect.com/science/article/pii/S0021869323005719?via%3Dihub. Acesso em: 08 ago. 2025.
Abstract:	Let F be a nilpotent group acted on by a group H via automorphisms and let the group G admit the semidirect product F H as a group of automorphisms so that CG(F) = 1. We prove that the order of γ∞(G), the rank of γ∞(G) are bounded in terms of the orders of γ∞(CG(H)) and H, the rank of γ∞(CG(H)) and the order of H, respectively in cases where either F H is a Frobenius group; F H is a Frobenius-like group satisfying some certain conditions; or F H = α, β is a dihedral group generated by the involutions α and β with F = αβ and H = α .
Unidade Acadêmica:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
DOI:	https://doi.org/10.1016/j.jalgebra.2023.11.011
Versão da editora:	https://www.sciencedirect.com/science/article/pii/S0021869323005719?via%3Dihub
Aparece nas coleções:	Artigos publicados em periódicos e afins

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