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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical logic, algebra and number theory
One corollary of description of finite groups without elements of order $6$
A. S. Kondrat'evab, M. S. Nirovac a N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS, S. Kovalevskaya St., 16, 620108, Yekaterinburg, Russia
b Ural Federal University, Ural Matematical Center, Mira St., 19, 620002, Yekaterinburg, Russia
c Kabardino-Balkarian State University named after H.M. Berbekov, Chernyshevsky St., 175, 360004, Nalchik, Russia
Abstract:
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, non-solvable group, Gruenberg-Kegel graph.
Received July 25, 2023, published October 26, 2023
Citation:
A. S. Kondrat'ev, M. S. Nirova, “One corollary of description of finite groups without elements of order $6$”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 854–858
Linking options:
https://www.mathnet.ru/eng/semr1615 https://www.mathnet.ru/eng/semr/v20/i2/p854
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