On finite groups in which commutators are covered by Engel subgroups-Reference-Cited by-同舟云学术

On finite groups in which commutators are covered by Engel subgroups

Published:2019-07-12 Issue:6 Volume:22 Page:1049-1057
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Shumyatsky Pavel¹,Silveira Danilo²

Affiliation:

1. Department of Mathematics , University of Brasilia , 70910-900 Brasília DF , Brazil

2. Department of Mathematics , Federal University of Goiás , 75704-020 Catalão GO , Brazil

Abstract

Abstract Let m , n

{m,n}

be positive integers and w a multilinear commutator word. Assume that G is a finite group having subgroups G 1 , … , G m

{G_{1},\ldots,G_{m}}

whose union contains all w-values in G. Assume further that all elements of the subgroups G 1 , … , G m

{G_{1},\ldots,G_{m}}

are n-Engel in G. It is shown that the verbal subgroup w ⁢ ( G )

{w(G)}

is s-Engel for some { m , n , w }

{\{m,n,w\}}

-bounded number s.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference21 articles.

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