Hyperzentrale Torsionsgruppen, deren Untergruppen alle subnormal sind. (Hypercentral torsion groups all subgroups of which are subnormal)
type: Item
instance of: scholarly article
title: Hyperzentrale Torsionsgruppen, deren Untergruppen alle subnormal sind. (Hypercentral torsion groups all subgroups of which are subnormal)
zbMATH Open document ID: 0697.20014
author: Walter Möhres
published in: Illinois Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: It is shown that a hypercentral torsion group with all subgroups subnormal is nilpotent. By an example of Heineken and Mohamed it is clear that the supposition of hypercentrality cannot be left, an example of H. Smith shows that the group also must be assumed to be periodic. For the proof two other results of the author are needed, namely that a group with all subgroups subnormal is soluble and that such a group if it additionally has finite exponent, is nilpotent.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 4142297
zbMATH Keywords: groups with all subgroups subnormal
zbMATH Keywords: hypercentral torsion group
zbMATH Keywords: nilpotent
zbMATH Keywords: soluble
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4142297