On locally finite groups factorized by locally nilpotent subgroups
type: Item
instance of: scholarly article
title: On locally finite groups factorized by locally nilpotent subgroups
zbMATH Open document ID: 0847.20037
DOI: 10.1016/0022-4049(95)00004-6
author: F. de Giovanni
author: Silvana Franciosi
author: Y. P. Sysak
published in: Journal of Pure and Applied Algebra
publication date: 1996-05-30T00:00:00Z
review text: The authors extend some well-known facts about finite products of two nilpotent subgroups to periodic radical groups \(G=AB\) which are the product of two locally nilpotent subgroups \(A\) and \(B\). For instance, it is shown that if \(A\) or \(B\) is hyperabelian and \(N\) is a minimal normal subgroup of \(G\), then one of the subgroups \(AN\) or \(BN\) is locally nilpotent. If \(A\) and \(B\) are nilpotent of classes \(c\) and \(d\), then the \((c+d+1)\)-th term of the derived series of \(G\) is locally nilpotent. If the periodic radical group \(G=AB=AC=BC\) is the product of three locally nilpotent subgroups \(A\), \(B\) and \(C\), at least one of which is hyperabelian, then \(G\) is locally nilpotent. The proofs of these results do not use that they are already known in the finite case [see the book ``Products of groups'' (1992; Zbl 0774.20001) by the first two authors and the reviewer].
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 858631
zbMATH Keywords: products of nilpotent subgroups
zbMATH Keywords: periodic radical groups
zbMATH Keywords: locally nilpotent subgroups
zbMATH Keywords: minimal normal subgroups
reviewed by: Bernhard Amberg
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00004-6
OpenAlex ID: W1985914921
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description: scientific article; zbMATH DE number 858631