Quasirecognition by prime graph of the groups \(^2 D_{2n}(q)\) where \(q<10^5\)
type: Item
instance of: scholarly article
title: Quasirecognition by prime graph of the groups \(^2 D_{2n}(q)\) where \(q<10^5\)
zbMATH Open document ID: 1402.20025
author: Hossein Moradi
author: M. R. Darafsheh
author: A. Iranmanesh
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: Let \(G\) be a finite group. The prime graph \(\Gamma (G)\) of \(G\) is defined as follows: The set of vertices of \(\Gamma (G)\) is the set of prime divisors of \(| G|\) and two distinct vertices \(p\) and \(p'\) are connected in \(\Gamma (G)\), whenever \(G\) contains an element of order \(pp'\). A non-abelian simple group \(P\) is called recognizable by prime graph if for any finite group \(G\) with \(\Gamma (G)=\Gamma (P)\), \(G\) has a composition factor isomorphic to \(P\). It is been proved that finite simple groups \(^2 D_n(q)\), where \(n \neq 4 k\), are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups \(^2 D_{2 k}(q)\), where \(k \geq 9\) and \(q\) is a prime power less than \(10^5\).
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 6898749
zbMATH Keywords: prime graph
zbMATH Keywords: simple group
zbMATH Keywords: orthogonal groups
zbMATH Keywords: quasirecognition
MaRDI profile type: Publication
full work available at URL: math6040057
OpenAlex ID: W2735868355
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DOI: 10.3390/MATH6040057
description: scientific article; zbMATH DE number 6898749