A characterization of \(\text{PSL}(3,q)\) where \(q\) is an odd prime power
type: Item
instance of: scholarly article
title: A characterization of \(\text{PSL}(3,q)\) where \(q\) is an odd prime power
zbMATH Open document ID: 1001.20005
DOI: 10.1016/S0022-4049(01)00113-X
author: A. Iranmanesh
author: Seyed Hassan Alavi
author: Behrooz Khosravi
published in: Journal of Pure and Applied Algebra
publication date: 2002-06-24T00:00:00Z
review text: Let \(G\) be a finite group and \(OC(G)\) the set of order components of \(G\) [\textit{G.-Y. Chen}, J. Algebra 185, No. 1, 184-193 (1996; Zbl 0861.20018)]. The authors prove that \(\text{PSL}(3,q)\) can be uniquely determined by its set of order components where \(q\) is an odd prime power. A main consequence of this result is the validity of Thompson's conjecture [see \textit{W.-J. Shi} and \textit{J.-X. Bi}, Lect. Notes Math. 1456, 171-180 (1990; Zbl 0718.20009)] for the groups under consideration.
reviewed by: Shi Wujie
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20E45
zbMATH DE Number: 1758361
zbMATH Keywords: simple groups of Lie type
zbMATH Keywords: order components
zbMATH Keywords: prime graphs
zbMATH Keywords: conjugacy classes
MaRDI profile type: Publication
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full work available at URL: s0022-4049(01)00113-x
OpenAlex ID: W1991860938
description: scientific article; zbMATH DE number 1758361