The \(p\)-intersection subgroups in quasi-simple and almost simple finite groups
type: Item
instance of: scholarly article
title: The \(p\)-intersection subgroups in quasi-simple and almost simple finite groups
zbMATH Open document ID: 0911.20015
author: Peter Fleischmann
author: Wolfgang Lempken
author: Pham Huu Tiep
published in: Journal of Algebra
publication date: 1999-03-01T00:00:00Z
review text: Let \(G\) be a finite group and \(p\) a prime number. A subgroup \(X\) is called a \(p\)-intersection group if \(X\cap X^g\) is a \(p\)-group for \(g\in G-X\), but \(X\) is not a \(p\)-group. In the paper under review all \(p\)-intersection groups \(X\) are determined when \(G\) is a quasi-simple or almost simple group. For the long list of such pairs \((G,X)\) we refer the reader to the paper itself. The authors of this article apply this result and classify [in Proc. Am. Math. Soc. 126, No. 5, 1337-1343 (1998; Zbl 0897.20003)] all primitive permutation groups in which a two-point stabilizer is a \(p\)-group.
reviewed by: Ulrich Dempwolff
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 1213845
zbMATH Keywords: finite groups
zbMATH Keywords: \(p\)-intersection groups
zbMATH Keywords: almost simple groups
MaRDI profile type: Publication
full work available at URL: jabr.1998.7431
OpenAlex ID: W2011357087
DOI: 10.1006/JABR.1998.7431
description: scientific article; zbMATH DE number 1213845