2-Engel relations between subgroups
type: Item
instance of: scholarly article
title: 2-Engel relations between subgroups
zbMATH Open document ID: 1371.20044
author: Peter Hauck
author: M. Pilar Gállego
author: M. D. Pérez-Ramos
published in: Journal of Algebra
publication date: 2015-12-07T00:00:00Z
review text: Two subgroups \(A\) and \(B\) of a group \(G\) are \textit{\(\mathcal{N}_{2}\)-connected} if, for all \(a \in A\) and \(b \in B\), the group \(\langle a,b \rangle\) is nilpotent of class at most two. This paper is devoted to the study of the groups \(G\) that are generated by two \(\mathcal{N}_{2}\)-connected subgroups \(A\) and \(B\). Under the previous assumption, the authors prove, among other things, that {\parindent=0.8cm \begin{itemize}\item[(i)] \([A,B]\) centralizes \(A'\) and \(B'\), \item[(ii)] \([A',B'] \leq Z(G)\), \item[(iii)] \([A^{2},B]\) is a normal subgroup of \(G\) contained in \(Z([A,B])\), \item[(iv)] \(A'\) is subnormal in \(G\) of defect at most \(3\) and \item[(v)] \(A^{2}\) is subnormal in \(G\) of defect at most \(3\) (here, \(A^{2}=\langle a^{2} \mid a \in A \rangle\)). \end{itemize}}
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 6517034
zbMATH Keywords: 2-Engel condition
zbMATH Keywords: commutator
zbMATH Keywords: \(\mathcal{N}_{2}\)-connection
zbMATH Keywords: nilpotency class
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2015.08.030
OpenAlex ID: W1827338102
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DOI: 10.1016/J.JALGEBRA.2015.08.030
description: scientific article; zbMATH DE number 6517034