Torsionsgruppen, deren Untergruppen alle subnormal sind. (Torsion groups all subgroups of which are subnormal)
type: Item
instance of: scholarly article
title: Torsionsgruppen, deren Untergruppen alle subnormal sind. (Torsion groups all subgroups of which are subnormal)
zbMATH Open document ID: 0675.20022
DOI: 10.1007/BF00147481
author: Walter Möhres
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: It is well-known that in a nilpotent group all subgroups are subnormal, but the converse is false. Here it is shown that a group G, which is an extension of a nilpotent torsion group by a soluble group of finite exponent and has all its subgroups subnormal, is nilpotent. The proof of this is easily reduced to the case where G is a p-group, which is an extension of an abelian normal subgroup by an elementary abelian group.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 4105214
zbMATH Keywords: soluble torsion groups
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: nilpotent group
zbMATH Keywords: extension
zbMATH Keywords: nilpotent torsion group
zbMATH Keywords: soluble group of finite exponent
reviewed by: Bernhard Amberg
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147481
OpenAlex ID: W2044627535
description: scientific article; zbMATH DE number 4105214