Recognition by spectrum of the groups \(^2D_{2^m+1}(3)\).
type: Item
instance of: scholarly article
title: Recognition by spectrum of the groups \(^2D_{2^m+1}(3)\).
zbMATH Open document ID: 1189.20026
author: Anatoli Kondrat'ev
published in: Science in China. Series A
publication date: 2009-12-07T00:00:00Z
review text: Let \(G\) be a finite group, and let \(\omega(G)\) denote the set of element orders of \(G\). The set \(\omega(G)\) is also called the spectrum of \(G\). For a natural number \(k\) a finite group \(G\) is called \(k\)-recognizable by spectrum if there are exactly \(k\) non-isomorphic groups \(H\) such that \(\omega(H)=\omega(G)\). If \(k=1\), the group \(G\) is called recognizable by spectrum. In the paper under review the author proves that the groups \(^2D_{2^m+1}(3)\) are recognizable by spectrum.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5643394
zbMATH Keywords: spectra of finite groups
zbMATH Keywords: prime graphs
zbMATH Keywords: finite simple groups
zbMATH Keywords: sets of element orders
zbMATH Keywords: recognizable groups
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: s11425-009-0010-1
OpenAlex ID: W1577810159
cites work: Prime graph components of finite groups
cites work: Q3032470
cites work: Q3565122
cites work: Q4551295
cites work: Q4416192
cites work: Q4449341
cites work: Quasirecognizability by the Set of Element Orders for Groups 3 D 4(q) and F 4(q), for q Odd
cites work: Quasirecognizability by the Set of Element Orders for Groups 3 D 4(q), for q Even
cites work: Q3545529
cites work: Q4764249
cites work: Q3708174
cites work: Q3684278
cites work: Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
cites work: Q4930353
cites work: Recognition of alternating groups of prime degree from their element orders
cites work: Q4369487
cites work: Centralizers of Semisimple Elements in the Finite Classical Groups
cites work: An Adjacency Criterion for the Prime Graph of a Finite Simple Group
cites work: On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group.
cites work: Q3996618
cites work: Singer-Zyklen in klassischen Gruppen
cites work: Finite simple unisingular groups of Lie type
cites work: Prime graph components of finite almost simple groups
cites work: Certain embeddings among finite groups of Lie type
DOI: 10.1007/S11425-009-0010-1
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description: scientific article; zbMATH DE number 5643394