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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 4, Pages 263–268
DOI: https://doi.org/10.21538/0134-4889-2021-27-4-263-268
(Mi timm1876)
 

This article is cited in 2 scientific papers (total in 2 papers)

Recognition of the Group $E_6(2)$ by Gruenberg-Kegel Graph

W. Guoab, A. S. Kondrat'evcde, N. V. Maslovacde

a School of Science, Hainan University
b School of Mathematical Sciences, University of Science and Technology of China
c N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
d Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
e Ural Mathematical Center, Yekaterinburg, 620000 Russia
Full-text PDF (147 kB) Citations (2)
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Abstract: The Gruenberg-Kegel graph (or the prime graph) of a finite group $G$ is a simple graph $\Gamma(G)$ whose vertices are the prime divisors of the order of $G$, and two distinct vertices $p$ and $q$ are adjacent in $\Gamma(G)$ if and only if $G$ contains an element of order $pq$. A finite group is called recognizable by Gruenberg-Kegel graph if it is uniquely determined up to isomorphism in the class of finite groups by its Gruenberg-Kegel graph. In this paper, we prove that the finite simple exceptional group of Lie type $E_6(2)$ is recognizable by its Gruenberg-Kegel graph.
Keywords: finite group; simple group; exceptional group of Lie type; Gruenberg-Kegel graph (prime graph).
Funding agency Grant number
National Natural Science Foundation of China 12171126
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1387
The work is supported by the National Natural Science Foundation of China (project No. 12171126), by Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences, and by the Regional Scientific and Educational Mathematical Center "Ural Mathematical Center" under the agreement No. 075-02-2021-1387 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 19.08.2021
Revised: 13.09.2021
Accepted: 17.09.2021
Bibliographic databases:
Document Type: Article
Language: English
Citation: W. Guo, A. S. Kondrat'ev, N. V. Maslova, “Recognition of the Group $E_6(2)$ by Gruenberg-Kegel Graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 4, 2021, 263–268
Citation in format AMSBIB
\Bibitem{GuoKonMas21}
\by W.~Guo, A.~S.~Kondrat'ev, N.~V.~Maslova
\paper Recognition of the Group $E_6(2)$ by Gruenberg-Kegel Graph
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 4
\pages 263--268
\mathnet{http://mi.mathnet.ru/timm1876}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-4-263-268}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000756004700018}
\elib{https://elibrary.ru/item.asp?id=47228431}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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