Quasirecognition by prime graph of \(F_4(q)\) where \(q=2^n>2\).
type: Item
instance of: scholarly article
title: Quasirecognition by prime graph of \(F_4(q)\) where \(q=2^n>2\).
zbMATH Open document ID: 1216.20007
published in: Monatshefte für Mathematik
publication date: 2011-03-31T00:00:00Z
review text: Let \(G\) be a finite group. The set of all primes dividing \(|G|\) is denoted by \(\pi(G)\). The prime graph \(\Gamma(G)\) of \(G\) is defined as follows: the vertices are the elements of \(\pi(G)\), and two distinct vertices \(p,q\) are joined by an edge if and only if there is an element of order \(pq\) in \(G\). The authors prove that if \(G\) is a finite group such that \(\Gamma(G)=\Gamma(F_4(q))\), where \(q=2^n>2\), then \(G\) has a unique nonabelian composition factor and this factor is isomorphic to \(F_4(q)\).
reviewed by: Anatoli Kondrat'ev
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5872786
zbMATH Keywords: non-Abelian composition factors
zbMATH Keywords: recognition of finite simple groups
zbMATH Keywords: sets of element orders
zbMATH Keywords: quasirecognizable groups
zbMATH Keywords: prime graphs
zbMATH Keywords: quasirecognition
author: Behrooz Khosravi
author: Azam Babai
MaRDI profile type: Publication
full work available at URL: s00605-009-0155-6
OpenAlex ID: W1969128811
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DOI: 10.1007/S00605-009-0155-6
description: scientific article; zbMATH DE number 5872786