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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
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).
Received: 19.08.2021 Revised: 13.09.2021 Accepted: 17.09.2021
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
Linking options:
https://www.mathnet.ru/eng/timm1876 https://www.mathnet.ru/eng/timm/v27/i4/p263
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