Geodesic
One corollary of description of finite groups without elements of order $6$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 854-858.

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Let $G$ be a finite group. The set of all prime divisors of the order of $G$ is denoted by $\pi(G)$. The Gruenberg-Kegel graph (the prime graph) $\Gamma(G)$ of $G$ is defined as the graph with the vertex set $\pi(G)$ in which two different vertices $p$ and $q$ are adjacent if and only if $G$ contains an element of order $pq$. If the order of $G$ is even, then $\pi_1(G)$ denotes the connected component of $\Gamma(G)$ containing $2$. It is actual the problem of describing finite groups with disconnected Gruenberg-Kegel graphs. In the present article, all finite non-solvable groups $G$ with $3 \in \pi(G)\setminus \pi_1(G)$ are determined.
Keywords: finite group, Gruenberg-Kegel graph.
Mots-clés : non-solvable group 
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A. S. Kondrat'ev; M. S. Nirova. One corollary of description of finite groups without elements of order $6$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 854-858. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a8/

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