Finite groups with seminormal Sylow subgroups.
type: Item
instance of: scholarly article
title: Finite groups with seminormal Sylow subgroups.
zbMATH Open document ID: 1176.20020
publication date: 2008-11-17T00:00:00Z
review text: The main result of this paper is the following: Let \(p\) be a prime number, \(P\) a Sylow \(p\)-subgroup of a group \(G\) and \(\pi=\pi(G)\setminus\{p\}\). If \(P\) is seminormal in \(G\), the following statements hold: (1) \(G\) is a \(p\)-soluble group and \(P'\leq O_p(G)\); (2) \(l_p(G)\leq 2\) and \(l_\pi(G)\leq 2\); (3) if a \(\pi\)-Hall subgroup of \(G\) is \(q\)-supersoluble for some \(q\in\pi\), then \(G\) is \(q\)-supersoluble. As Michael C. Slattery wrote in his review of this paper for the Mathematical Reviews, the results all seem to follow from the nice and interesting results in [\textit{V. S. Monakhov}, Mat. Zametki 80, No. 4, 573-581 (2006; Zbl 1128.20011)], which is not cited. Furthermore, the wording, sentence structure, paragraph structure and theorem statements in Guo's paper are very similar to those in Monakhov's paper. In fact, the results of Monakhov are more general since he deals with Hall subgroups.
reviewed by: Adolfo Ballester-Bolinches
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 5366767
zbMATH Keywords: finite groups
zbMATH Keywords: seminormal subgroups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: \(p\)-soluble groups
zbMATH Keywords: \(p\)-supersoluble groups
author: Wenbin Guo
MaRDI profile type: Publication
full work available at URL: s10114-008-6563-z
OpenAlex ID: W2125618904
cites work: Q4205635
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DOI: 10.1007/S10114-008-6563-Z
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5366767