Finite groups with subgroups supersoluble or subnormal.
type: Item
instance of: scholarly article
title: Finite groups with subgroups supersoluble or subnormal.
zbMATH Open document ID: 1172.20018
author: Adolfo Ballester-Bolinches
author: John Cossey
published in: Journal of Algebra
publication date: 2009-06-08T00:00:00Z
review text: The paper studies the structure of finite groups whose non-subnormal subgroups lie in some subclasses of the class \(\mathcal U\) of finite supersoluble groups. These subclasses are \(\mathcal U\) itself, the class of PST-groups (i.e. groups in which the property of permuting with Sylow subgroups is transitive), the class of PT-groups (i.e. groups in which permutability is transitive) and the class of T-groups (i.e. groups in which normality of subgroups is transitive). For each of these classes the authors give a detailed description of the possible structure of such groups. They show that there is a complemented chief factor with complement in the given class and that it is easy to construct examples to show that a group with a complemented chief factor having a complement in the given class is not sufficient to ensure that all non-subnormal subgroups lie in the given class. The paper analyses the way in which a complement acts on the complemented chief factor and describes this action in enough detail to characterize the groups in each class.
reviewed by: Rodica Covaci
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 5562709
zbMATH Keywords: finite groups
zbMATH Keywords: finite soluble groups
zbMATH Keywords: finite supersoluble groups
zbMATH Keywords: PST-groups
zbMATH Keywords: PT-groups
zbMATH Keywords: T-groups
zbMATH Keywords: transitive normality
zbMATH Keywords: permutable subgroups
zbMATH Keywords: complemented chief factors
zbMATH Keywords: complemented subgroups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.12.023
OpenAlex ID: W2065653654
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DOI: 10.1016/J.JALGEBRA.2008.12.023
description: scientific article; zbMATH DE number 5562709