Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal)
type: Item
instance of: scholarly article
title: Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. (Solubility of groups all subgroups of which are subnormal)
zbMATH Open document ID: 0663.20027
DOI: 10.1007/BF01188516
author: Walter Möhres
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: A proof is given that a group with all subgroups subnormal is soluble. This is a generalization of a theorem of C. Casolo which says that the derived series of such a group ends after a finite number of steps. Moreover it is shown that the Fitting subgroup of a group with all subgroups subnormal contains its torsion subgroup.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 4083908
zbMATH Keywords: derived series
zbMATH Keywords: Fitting subgroup
zbMATH Keywords: torsion subgroup
zbMATH Keywords: groups with all subgroups subnormal
zbMATH Keywords: solubility of groups
MaRDI profile type: Publication
cites work: Groups with every Subgroup Subnormal
cites work: Q3748466
cites work: Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind. (Torsion free groups all of whose subgroups are subnormal)
cites work: Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormal sind. II. (Soluble groups of finite exponent all subgroups of which are subnormal. II)
cites work: Q3941589
cites work: On groups in which every subgroup is subnormal
full work available at URL: https://doi.org/10.1007/bf01188516
OpenAlex ID: W2023186803
description: scientific article; zbMATH DE number 4083908