A criterion for subnormality and Wielandt complexes in finite groups
type: Item
instance of: scholarly article
title: A criterion for subnormality and Wielandt complexes in finite groups
zbMATH Open document ID: 0812.20007
author: Carlo Casolo
published in: Journal of Algebra
publication date: 1994-11-06T00:00:00Z
review text: This paper illustrates the power of the classification of finite simple groups to problems in group theory which appear to have no connection with finite simple groups. The main theorem is the following. Let \(G\) be a finite group and \(H\) a subgroup of \(G\). Suppose that for each prime \(p\) dividing the order of \(G\) there is a Sylow \(p\)-subgroup of \(G\), \(G_ p\), such that \(H\) is subnormal in \(\langle G_ p, H\rangle\). Then \(H\) is a subnormal subgroup of \(G\). The proof depends on reducing the problem to one concerning finite simple groups. The author then uses this theorem to consider a problem of subnormality in infinite groups related to the Wielandt complex.
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 682586
zbMATH Keywords: classification of finite simple groups
zbMATH Keywords: Sylow \(p\)-subgroup
zbMATH Keywords: subnormal subgroup
zbMATH Keywords: subnormality in infinite groups
zbMATH Keywords: Wielandt complex
reviewed by: A. R. Camina
MaRDI profile type: Publication
full work available at URL: jabr.1994.1299
OpenAlex ID: W1990713566
DOI: 10.1006/JABR.1994.1299
description: scientific article; zbMATH DE number 682586