Almost recognizability by spectrum of finite simple linear groups of prime dimension.
type: Item
instance of: scholarly article
title: Almost recognizability by spectrum of finite simple linear groups of prime dimension.
zbMATH Open document ID: 1270.20011
DOI: 10.1134/S0037446612040076
published in: Siberian Mathematical Journal
publication date: 2012-11-14T00:00:00Z
review text: Let \(G\) be a finite group. The spectrum of \(G\) is the set of element orders of \(G\) and is denoted by \(w(G)\). The recognition problem for \(G\) is to determine the number of isomorphism classes of finite groups \(H\) with \(w(H)=w(G)\). The main result of the paper under review is that if \(L=\text{PSL}(n,q)\) where \(n\) is a prime greater than 3 and if \(G\) is finite group with \(w(L)=w(G)\), then \(L<G<\Aut\,L\). This implies that the number of isomorphism classes of the group \(G\) is finite, i.e. the group \(L\) is almost recognizable by the set of element orders.
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 6105712
zbMATH Keywords: simple linear groups
zbMATH Keywords: prime graphs
zbMATH Keywords: quasirecognizability by spectrum
zbMATH Keywords: spectra of finite groups
zbMATH Keywords: sets of element orders
zbMATH Keywords: finite simple groups
zbMATH Keywords: quasirecognizable groups
author: Mariya A. Grechkoseeva
author: Daniil Vsevolodovich Lytkin
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
cites work: Q4292041
cites work: Q3565122
cites work: Recognition of the simple groups L3(q) by element orders
cites work: Recognition of simple groups U 3(Q) by element orders
cites work: Q3538808
cites work: Recognizability of finite simple groups L 4(2m) and U 4(2m) by spectrum
cites work: Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2
cites work: Recognition of the projective special linear group over \(\text{GF}(3)\).
cites work: Recognition of alternating groups of prime degree from their element orders
cites work: Prime graph components of finite groups
cites work: Spectra of finite linear and unitary groups
cites work: Large element orders and the characteristic of Lie-type simple groups.
cites work: Cocliques of maximal size in the prime graph of a finite simple group
cites work: On finite groups isospectral to simple linear and unitary groups.
cites work: Spectra of finite symplectic and orthogonal groups.
cites work: Prime power graphs for groups of Lie type
cites work: The maximal subgroups of the Chevalley groups \(G_ 2(q)\) with q odd, the Ree groups \(2G_ 2(q)\), and their automorphism groups
cites work: Maximal subgroups of \(G_2(2^n)\)
cites work: Prime graph components of finite almost simple groups
cites work: Addendum to ``Prime graph components of finite almost simple groups''.
cites work: On the existence of a complement for a finite simple group in its automorphism group
cites work: Q4375273
description: scientific article; zbMATH DE number 6105712