On finite groups in which commutators are covered by Engel subgroups

Pavel Shumyatsky; Danilo Silveira

On finite groups in which commutators are covered by Engel subgroups

Group Theory 2019-01-08 v1

Authors: Pavel Shumyatsky , Danilo Silveira

Abstract

Let $m,n$ be positive integers and $w$ a multilinear commutator word. Assume that $G$ is a finite group having subgroups $G_1,\ldots,G_m$ whose union contains all $w$ -values in $G$ . Assume further that all elements of the subgroups $G_1,\ldots,G_m$ are $n$ -Engel in $G$ . It is shown that the verbal subgroup $w(G)$ is $s$ -Engel for some $\{m,n,w\}$ -bounded number $s$ .

Keywords

finite group theory group theory representation theory of groups

Cite

@article{arxiv.1901.01859,
  title  = {On finite groups in which commutators are covered by Engel subgroups},
  author = {Pavel Shumyatsky and Danilo Silveira},
  journal= {arXiv preprint arXiv:1901.01859},
  year   = {2019}
}

Comments

9 pages. arXiv admin note: text overlap with arXiv:1702.02899, arXiv:1602.01661

On finite groups in which commutators are covered by Engel subgroups

Abstract

Keywords

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