Recognition of simple groups \(B_p(3)\) by the set of element orders.
type: Item
instance of: scholarly article
title: Recognition of simple groups \(B_p(3)\) by the set of element orders.
zbMATH Open document ID: 1210.20020
author: Shi Wujie
author: M. R. Zinov'eva
author: Rulin Shen
published in: Siberian Mathematical Journal
publication date: 2010-11-15T00:00:00Z
review text: Let \(G\) be a finite group. The set of element orders of \(G\) is denoted by \(\omega(G)\) and is called the spectrum of \(G\). Given a natural number \(k\), a group \(G\) is said to be \(k\)-recognizable by spectrum if there are \(k\) non-isomorphic groups \(H\) such that \(\omega(H)=\omega(G)\). If \(k=1\), the group \(G\) is called recognizable by spectrum. In the present paper the authors consider the simple group \(B_p(3)\), where \(p\) is an odd prime, and prove that if \(p>3\) then the group \(B_p(3)\) is recognizable by spectrum and if \(p=3\), then \(B_3(3)\) is 2-recognizable by spectrum.
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5816237
zbMATH Keywords: finite orthogonal groups
zbMATH Keywords: sets of element orders
zbMATH Keywords: prime graphs
zbMATH Keywords: recognition by spectrum
MaRDI profile type: Publication
full work available at URL: s11202-010-0024-5
OpenAlex ID: W2167558232
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DOI: 10.1007/S11202-010-0024-5
description: scientific article; zbMATH DE number 5816237