Properties of a finite group representable as the product of two nilpotent groups
type: Item
instance of: scholarly article
zbMATH Open document ID: 0992.20016
DOI: 10.1023/A:1012330805877
author: N. S. Chernikov
publication date: 2001-11-04T00:00:00Z
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 1668443
zbMATH Keywords: finite groups
zbMATH Keywords: products of subgroups
zbMATH Keywords: nilpotent subgroups
zbMATH Keywords: Fitting subgroups
zbMATH Keywords: derived lengths
MaRDI profile type: Publication
full work available at URL: a:1012330805877
OpenAlex ID: W64195476
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published in: Ukraïns'kyĭ Matematychnyĭ Zhurnal
title: Properties of a finite group representable as the product of two nilpotent groups
review text: The author studies finite groups \(G=AB\), where \(A\) and \(B\) are nilpotent subgroups. The main theorem gives some properties of the factor-group \(G/F(G)\) (\(F(G)\) is the Fitting subgroup of \(G\), i.e. the product of all normal nilpotent subgroups of \(G\)). In particular, it is shown that the nilpotent coradical of the group \(G/F(G)\) coincides with the subgroup \([A,B]F(G)/F(G)\) and the intersection \(A\cap B\) is contained in \(H=[A,B]F(G)\) (the last normal subgroup can be written in the form \(H=(H\cap A)(H\cap B)\)).
description: scientific article; zbMATH DE number 1668443