The influence of \(\mathcal M\)-supplemented subgroups on the structure of finite groups.
type: Item
instance of: scholarly article
title: The influence of \(\mathcal M\)-supplemented subgroups on the structure of finite groups.
zbMATH Open document ID: 1194.20015
author: Long Miao
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2009-12-02T00:00:00Z
review text: From the author's summary: A subgroup \(H\) of a finite group \(G\) is said to be \(\mathcal M\)-supplemented in \(G\) if there exists a subgroup \(B\) of \(G\) such that \(G=HB\) and \(TB<G\) for every maximal subgroup \(T\) of \(H\). Moreover, a subgroup \(H\) is called \(c\)-supplemented in \(G\) if there exists a subgroup \(K\) such that \(G=HK\) and \(H\cap K\leq H_G\) where \(H_G\) is the largest normal subgroup of \(G\) contained in \(H\). In this paper the author gives some conditions to guarantee the supersolubility of a finite group, under the assumption that some primary subgroups have some kinds of supplements. He also obtains some extensions by considering saturated formations containing the class \(\mathcal U\) of all supersoluble groups, which are generalizations of some recent results.
reviewed by: Ana Martínez-Pastor
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 5641447
zbMATH Keywords: finite groups
zbMATH Keywords: supersoluble groups
zbMATH Keywords: saturated formations
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: primary subgroups
zbMATH Keywords: supplemented subgroups
MaRDI profile type: Publication
full work available at URL: s00574-009-0024-x
OpenAlex ID: W1981640306
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DOI: 10.1007/S00574-009-0024-X
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description: scientific article; zbMATH DE number 5641447