A characterization of \(\text{PSU}_3(q)\) for \(q>5\)
type: Item
instance of: scholarly article
title: A characterization of \(\text{PSU}_3(q)\) for \(q>5\)
zbMATH Open document ID: 1019.20012
author: A. Iranmanesh
author: Behrooz Khosravi
author: Seyed Hassan Alavi
published in: Southeast Asian Bulletin of Mathematics
publication date: 2003-03-18T00:00:00Z
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)]. In this paper the authors prove that \(\text{PSU}(3,q)\) where \(q>5\) can be uniquely determined by its set of order components. A main consequence (Corollary 3.2) of this result is the validity of Thompson's conjecture for the groups under consideration. Corollary 3.4 is proved for the general case of finite unitary groups of any dimension by reviewer and \textit{H.-P. Cao} [Pure quantitative characterization of finite projective special unitary groups, Sci. China, Ser. A 45, No. 6, 761-772 (2002)].
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1884048
zbMATH Keywords: simple groups of Lie type
zbMATH Keywords: prime graphs
zbMATH Keywords: order components
reviewed by: Shi Wujie
MaRDI profile type: Publication
full work available at URL: s100120200024
OpenAlex ID: W2007204297
DOI: 10.1007/S100120200024
description: scientific article; zbMATH DE number 1884048