Characterization of groups $E_6(3)$ and ${^2}E_6(3)$ by Gruenberg--Kegel graph
| Autor: | Khramova, A. P., Maslova, N. V., Panshin, V. V., Staroletov, A. M. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $G\cong L$. Comment: Corrected graph pictures. 6 pages |
| Databáze: | arXiv |
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