Thompson's conjecture for simple groups with connected prime graph.
type: Item
instance of: scholarly article
title: Thompson's conjecture for simple groups with connected prime graph.
zbMATH Open document ID: 1270.20010
published in: Algebra and Logic
publication date: 2012-12-11T00:00:00Z
review text: Question 12.38 in The Kourovka notebook [2010; Zbl 1211.20001] states that: Let \(N(G)\) denote the set of all orders of the conjugacy class sizes in a finite group \(G\). Is it true that if \(G\) is a finite nonabelian simple group, \(H\) a finite group with trivial centre and \(N(G)=N(H)\) then \(G\) and \(H\) are isomorphic? This question is known as the Thompson conjecture. In the paper under review the author considers finite nonabelian simple groups \(G\) where the prime divisors of the order of \(G\) are numbers in the set \(S=\{2,3,5,7,11,13,17\}\), and verifies Thompson's conjecture for these groups. Although the conjecture was already verified for some of these groups, but the present paper completes the conjecture for finite nonabelian simple groups with order divisible by primes in \(S\).
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 6115027
zbMATH Keywords: finite simple groups
zbMATH Keywords: conjugacy class sizes
zbMATH Keywords: Thompson conjecture
author: Ilya B. Gorshkov
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: s10469-012-9175-8
OpenAlex ID: W1964016548
Wikidata QID: Q123111219
cites work: Q3084921
cites work: Prime graph components of finite groups
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cites work: On Thompson's conjecture
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cites work: Finite simple groups with narrow prime spectrum.
cites work: An Adjacency Criterion for the Prime Graph of a Finite Simple Group
cites work: Q3684278
cites work: Q5476747
DOI: 10.1007/S10469-012-9175-8
description: scientific article; zbMATH DE number 6115027