Аннотация:
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 $G\cong L$.
Ключевые слова:finite group, simple group, the Gruenberg–Kegel graph, exceptional group of Lie type $E_6$.