Geodesic
Characterization of groups $E_6(3)$ and ${^2}E_6(3)$ by Gruenberg--Kegel graph
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1651-1656

Voir la notice de l'article provenant de la source Math-Net.Ru

The Gruenberg–Kegel graph (or the prime graph) $\Gamma(G)$ of a finite group $G$ is defined as follows. The vertex set of $\Gamma(G)$ is the set of all prime divisors of the order of $G$. Two distinct primes $r$ and $s$ regarded as vertices are adjacent in $\Gamma(G)$ if and only if there exists an element of order $rs$ in $G$. Suppose that $L\cong E_6(3)$ or $L\cong{}^2E_6(3)$. We prove that if $G$ is a finite group such that $\Gamma(G)=\Gamma(L)$, then $G\cong L$.
Keywords: finite group, the Gruenberg–Kegel graph, exceptional group of Lie type $E_6$.
Mots-clés : simple group 
@article{SEMR_2021_18_2_a13,
     author = {A. P. Khramova and N. V. Maslova and V. V. Panshin and A. M. Staroletov},
     title = {Characterization of groups $E_6(3)$ and ${^2}E_6(3)$ by {Gruenberg--Kegel} graph},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1651--1656},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a13/}
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A. P. Khramova; N. V. Maslova; V. V. Panshin; A. M. Staroletov. Characterization of groups $E_6(3)$ and ${^2}E_6(3)$ by Gruenberg--Kegel graph. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1651-1656. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a13/