Minimal normal subgroups of dinilpotent groups
type: Item
instance of: scholarly article
title: Minimal normal subgroups of dinilpotent groups
zbMATH Open document ID: 0976.20021
published in: Journal of Algebra
publication date: 2001-05-03T00:00:00Z
review text: A group \(G\) is said to be dinilpotent if it has a nilpotent factorization, i.e., if \(G=AB\), where \(A\) and \(B\) are nilpotent subgroups of \(G\). It was proved by \textit{S. E. Stonehewer} [J. Pure Appl. Algebra 88, No. 1-3, 239-244 (1993; Zbl 0784.20012)] that if \(N\) is a minimal normal subgroup of a finite dinilpotent group \(G=AB\), then at least one of the subgroups \(AN\) and \(BN\) is nilpotent. In this article the authors extend this result to several classes of infinite groups. In particular, they show that if the dinilpotent group \(G=AB\) is nilpotent-by-polycyclic and \(A\cap B\) is periodic, then either \(AN\) or \(BN\) is nilpotent for every minimal normal subgroup \(N\) of \(G\). Some consequences of this theorem are also proved.
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 1565870
zbMATH Keywords: factorized groups
zbMATH Keywords: nilpotent groups
zbMATH Keywords: minimal normal subgroups
zbMATH Keywords: nilpotent factorizations
author: Derek J. S. Robinson
author: Stewart Stonehewer
MaRDI profile type: Publication
full work available at URL: jabr.2000.8551
OpenAlex ID: W2066915108
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DOI: 10.1006/JABR.2000.8551
description: scientific article; zbMATH DE number 1565870