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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1378–1382 (Mi semr1003)  

Mathematical logic, algebra and number theory

Finite almost simple groups whose Gruenberg–Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of the alternating group $A_{10}$

A. S. Kondrat'ev, N. A. Minigulov

N.N. Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaya St., 16, 620990, Yekaterinburg, Russia

Abstract: We consider the problem of describing finite groups whose the Gruenberg-Kegel graphs as abstract graphs are isomorphic to the Gruenberg–Kegel graph of the alternating group $A_{10}$. In the given paper, we prove that if such group is non-solvable then its quotient group by solvable radical is almost simple and classify all finite almost simple groups whose the Gruenberg-Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of $A_{10}$.

Keywords: finite group, almost simple group, 4-primary group, Gruenberg–Kegel graph.

Funding Agency Grant Number
Russian Science Foundation 14-11-00061-P
The work is supported by the Russian Science Foundation (project 14-11-00061-P).


DOI: https://doi.org/10.17377/semi.2018.15.113

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Document Type: Article
UDC: 512.54
MSC: 20D60, 05C25
Received September 30, 2018, published November 7, 2018
Language: English

Citation: A. S. Kondrat'ev, N. A. Minigulov, “Finite almost simple groups whose Gruenberg–Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of the alternating group $A_{10}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 1378–1382

Citation in format AMSBIB
\Bibitem{KonMin18}
\by A.~S.~Kondrat'ev, N.~A.~Minigulov
\paper Finite almost simple groups whose Gruenberg--Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg--Kegel graph of the alternating group $A_{10}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1378--1382
\mathnet{http://mi.mathnet.ru/semr1003}
\crossref{https://doi.org/10.17377/semi.2018.15.113}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200055}


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