Recognition of alternating groups of prime degree from their element orders
type: Item
instance of: scholarly article
title: Recognition of alternating groups of prime degree from their element orders
zbMATH Open document ID: 0956.20007
DOI: 10.1007/BF02674599
author: Anatoli Kondrat'ev
author: V. D. Mazurov
published in: Siberian Mathematical Journal
publication date: 2000-11-21T00:00:00Z
full work available at URL: https://eudml.org/doc/120815
review text: Let \(G\) be a group. The set of the orders of the elements is denoted by \(\omega(G)\). The following theorem is proven: Let \(G\) be a finite group such that \(\omega(G)=\omega(A_r)\), where \(A_r\) is the alternating group of degree \(r\) and \(r>3\) is a prime. Then \(G\cong A_r\). Recently, A. V. Zavarnitsyn generalized this result and proved an analogous theorem for the alternating group \(A_r\), where either \(r=p+1\) or \(r=p+2\) and \(p>7\) is a prime.
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 1534389
zbMATH Keywords: prime graphs
zbMATH Keywords: Gruenberg-Kegel graphs
zbMATH Keywords: finite simple groups
zbMATH Keywords: alternating groups
zbMATH Keywords: element orders
MaRDI profile type: Publication
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OpenAlex ID: W2030121754
description: scientific article; zbMATH DE number 1534389