On Thompson's conjecture
type: Item
instance of: scholarly article
title: On Thompson's conjecture
zbMATH Open document ID: 0861.20018
published in: Journal of Algebra
publication date: 1997-05-13T00:00:00Z
review text: For a finite group \(G\), \(N(G)\) denotes the set of the orders of conjugacy classes of \(G\). J. G. Thompson has conjectured that if \(G\) is a finite group with \(Z(G)=1\) and \(M\) is a finite nonabelian simple group with \(N(G)=N(M)\), then \(G\cong M\). In [Proc. China Assoc. Sci. Tech. First. Acad. Ann. Meeting of Youths, 1-6, Chin. Sci. Tech. Press, Beijing (1992)], the author has proved that if \(M\) is a sporadic simple group, then Thompson's conjecture is valid. In this paper, he proves the validity of the conjecture for each finite simple group \(M\) having at least three prime graph components. The proof is based on the classification of prime graph components of (known) finite simple groups given by \textit{J. S. Williams} [J. Algebra 69, 487-513 (1981; Zbl 0471.20013)] and the reviewer [Mat. Sb. 180, No. 6, 787-797 (1989; Zbl 0691.20013)].
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 941231
zbMATH Keywords: Thompson conjecture
zbMATH Keywords: orders of conjugacy classes
zbMATH Keywords: prime graph components
zbMATH Keywords: finite simple groups
Wikidata QID: Q122876616
author: Guiyun Chen
reviewed by: Anatoli Kondrat'ev
MaRDI profile type: Publication
full work available at URL: jabr.1996.0320
OpenAlex ID: W1987194282
DOI: 10.1006/JABR.1996.0320
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description: scientific article; zbMATH DE number 941231