Finite groups with certain subgroups of Sylow subgroups complemented.
type: Item
instance of: scholarly article
title: Finite groups with certain subgroups of Sylow subgroups complemented.
zbMATH Open document ID: 1202.20028
published in: Journal of Algebra
publication date: 2010-04-21T00:00:00Z
review text: Let \(\mathcal I\) be a saturated formation containing the class of supersoluble groups, \(G\) be a finite group with a normal subgroup \(E\) such that \(G/E\in\mathcal I\), and \(F^*(E)\) the generalised Fitting subgroup of \(E\). Theorem 1.3: If \(P\) is a Sylow subgroup of \(E\) and \(P\) has a proper subgroup \(D\) such that each subgroup \(H\) of \(P\) which is satisfying \({|H|\over|D|}= 1\) or \({|H|\over|D|}=\) a prime is complemented in \(G\), then \(G\in\mathcal I\). If \(P\) is a Sylow subgroup of \(F^*(E)\) and \(P\) has a proper subgroup \(D\) such that each subgroup \(H\) of \(P\) which is satisfying \({|H|\over|D|}= 1\) or \({|H|\over|D|}=\) a prime is complemented in \(G\), then \(G\in\mathcal I\) (Theorem 1.4).
reviewed by: Hans Lausch
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 5696930
zbMATH Keywords: complements
zbMATH Keywords: saturated formations
zbMATH Keywords: Sylow subgroups
author: M. Asaad
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.02.006
OpenAlex ID: W2035936682
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DOI: 10.1016/J.JALGEBRA.2010.02.006
description: scientific article; zbMATH DE number 5696930