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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 854–858
DOI: https://doi.org/10.33048/semi.2023.20.052
(Mi semr1615)
 

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
Full-text PDF (373 kB) Citations (1)
References:
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-935
Received July 25, 2023, published October 26, 2023
Document Type: Article
UDC: 512.54
MSC: 20D60, 05C25
Language: Russian
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
Citation in format AMSBIB
\Bibitem{KonNir23}
\by A.~S.~Kondrat'ev, M.~S.~Nirova
\paper One corollary of description of finite groups without elements of order $6$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 854--858
\mathnet{http://mi.mathnet.ru/semr1615}
\crossref{https://doi.org/10.33048/semi.2023.20.052}
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