A proof of the Kegel-Wielandt conjecture on subnormal subgroups
type: Item
instance of: scholarly article
title: A proof of the Kegel-Wielandt conjecture on subnormal subgroups
zbMATH Open document ID: 0726.20012
DOI: 10.2307/2944342
author: Peter B. Kleidman
published in: Annals of Mathematics. Second Series
publication date: 1991-01-01T00:00:00Z
review text: Using the classification of the finite simple groups the author proves the following theorem which appears as a conjecture in papers of \textit{O. H. Kegel} [Math. Z. 78, 205-221 (1962; Zbl 0102.26802)] and \textit{H. Wielandt} [Proc. Symp. Pure Math. 37, 161-173 (1980; Zbl 0458.20024)]: Let \(G\) be a finite group and \(H\) a subgroup of \(G\). Then \(H\) is subnormal in \(G\) if and only if for all primes \(p\), every Sylow \(p\)-subgroup of \(G\) intersects \(H\) in a Sylow \(p\)-subgroup of \(H\).
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 4198308
zbMATH Keywords: finite groups
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: Sylow subgroups
Wikidata QID: Q123080323
reviewed by: V. D. Mazurov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2944342
OpenAlex ID: W2326972670
description: scientific article; zbMATH DE number 4198308