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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 111–121 (Mi semr659)  

Mathematical logic, algebra and number theory

On recognition by spectrum of symmetric groups

I. B. Gorshkova, A. N. Grishkovb

a N. N. Krasovskii Institute of Mathematics and Mechanics, 16, S. Kovalevskaja St, 620990, Ekaterinburg, Russia
b Instituto de Matematica e Statistica, Universidade de Sao Paulo, R. do Matao, 1010 - Vila Universitaria, 05508-090, Sao Paulo, Brasil

Abstract: The spectrum of a group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group with the same spectrum is isomorphic to $G$. We prove that if $n\in\{15,16,18,21,27\}$ then symmetric groups $Sym_n$ are recognizable by spectrum.

Keywords: finite group, simple group, symmetric group, spectrum of a group, recognizability by spectrum.

Funding Agency Grant Number
Fundação de Amparo à Pesquisa do Estado de São Paulo 2014/08964-1
Ministry of Education and Science of the Russian Federation MK-6118.2016.1
Russian Foundation for Basic Research 13-01-00239_a
The work is supported by the FAPESP (grant no. 2014/08964-1), by the grant of the President of Russian Federation for young scientists (grants no. MKMK-6118.2016.1), by the RFFI (grant no. 13-01-00239a).


DOI: https://doi.org/10.17377/semi.2016.13.009

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Bibliographic databases:

UDC: 512.542
MSC: 20D05
Received March 13, 2015, published February 26, 2016
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Citation: I. B. Gorshkov, A. N. Grishkov, “On recognition by spectrum of symmetric groups”, Sib. Èlektron. Mat. Izv., 13 (2016), 111–121

Citation in format AMSBIB
\Bibitem{GorGri16}
\by I.~B.~Gorshkov, A.~N.~Grishkov
\paper On recognition by spectrum of symmetric groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 111--121
\mathnet{http://mi.mathnet.ru/semr659}
\crossref{https://doi.org/10.17377/semi.2016.13.009}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000407781100010}


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