Quasirecognition by prime graph of the simple group \(^2F_4(q)\).
type: Item
instance of: scholarly article
title: Quasirecognition by prime graph of the simple group \(^2F_4(q)\).
zbMATH Open document ID: 1181.20012
published in: Acta Mathematica Hungarica
publication date: 2009-12-28T00:00:00Z
review text: The prime graph \(\Gamma(G)\) of a finite group \(G\) is constructed as follows. Its vertex set consists of the set containing the prime divisors of the order of \(G\) and two distinct primes \(p\) and \(q\) are joined by an edge if and only if \(G\) contains an element of order \(pq\). In this paper it is shown that \(\Gamma(G)=\Gamma(^2F_4(2^{2m+1}))\) implies that \(G\) has a unique non-Abelian composition factor isomorphic to \(^2F_4(2^{2m+1})\); hence \(m\geq 1\). Moreover, if \(G\) is some finite group whose order is equal to that of \(^2F_4(2^{2m+1})\) and for which \(\Gamma(G)=\Gamma(^2 F_4(2^{2m+1}))\) also holds, then \(G\) must be isomorphic to \(^2F_4(2^{2m+1})\).
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5651867
zbMATH Keywords: quasirecognition
zbMATH Keywords: prime graphs
zbMATH Keywords: finite simple groups
zbMATH Keywords: element orders
author: Z. Akhlaghi
author: M. Khatami
author: Behrooz Khosravi
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
DOI: 10.1007/S10474-008-8048-7
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description: scientific article; zbMATH DE number 5651867