Further reflections on Thompson's conjecture
type: Item
instance of: scholarly article
title: Further reflections on Thompson's conjecture
zbMATH Open document ID: 0931.20020
published in: Journal of Algebra
publication date: 1999-11-29T00:00:00Z
review text: Let \(G\) be a finite group and let \(N(G)\) be the set of orders of all conjugacy classes of \(G\). J.~G.~Thompson has conjectured that if \(Z(G)=1\) and \(M\) is a non-abelian simple group with \(N(G)=N(M)\) then \(G\cong M\). In previous papers [Algebra Colloq. 3, No. 1, 49-58 (1996; Zbl 0845.20011) and J. Algebra 185, No. 1, 184-193 (1996; Zbl 0861.20018)], the author proved Thompson's conjecture in the case when \(M\) is a sporadic simple group or a simple group with at least three prime graph components. In this paper, he proves Thompson's conjecture for \(M\cong G_2(q)\).
reviewed by: Anatoli Kondrat'ev
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1340583
zbMATH Keywords: finite groups
zbMATH Keywords: orders of conjugacy classes
zbMATH Keywords: orders of elements
zbMATH Keywords: prime graph components
zbMATH Keywords: finite simple groups
author: Guiyun Chen
MaRDI profile type: Publication
full work available at URL: jabr.1998.7839
OpenAlex ID: W2048935891
Wikidata QID: Q123153286
cites work: Q4320116
cites work: Q4869726
cites work: On Thompson's conjecture
cites work: Q3684278
cites work: PRIME GRAPH COMPONENTS OF FINITE SIMPLE GROUPS
cites work: Prime graph components of finite groups
DOI: 10.1006/JABR.1998.7839
description: scientific article; zbMATH DE number 1340583