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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 1, Pages 65–71
DOI: https://doi.org/10.33048/smzh.2023.64.106 (Mi smj7745) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Finite groups whose prime graphs do not contain triangles. III

W. Guoab, M. R. Zinov'evacd, A. S. Kondrat'evcd

a University of Science and Technology of China, Anhui, Hefei
b Hainan University
c N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
d Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.33048/smzh.2023.64.106
Abstract: The prime graph or the Gruenberg–Kegel graph of a finite group $G$ is the graph whose vertices are the prime divisors of the order of $G$ and two distinct vertices $p$ and $q$ are adjacent if and only if $G$ contains an element of order $pq$. This paper continues the study of the problem of describing the finite nonsolvable groups whose prime graphs do not contain triangles. We describe the groups in the case when a group has an element of order $6$ and the order of its solvable radical is divisible by a prime greater than $3$.
Keywords: finite group, nonsolvable group, prime graph or Gruenberg–Kegel graph without triangles.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-53013
National Natural Science Foundation of China 12171126
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
This research was supported by the Russian Foundation for Basic Research and the NNSF of China in the framework of the joint Project 20–51–53013, by the NNSF of China in the framework of the Project 12171126, and the State Maintenance Program for the Leading Universities of the Russian Federation (Agreement 02.A03.21.0006 of 27.08.2013).
Received: 15.03.2022
Revised: 29.08.2022
Accepted: 10.10.2022
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 1, Pages 56–61
DOI: https://doi.org/10.1134/S0037446623010068
Document Type: Article
UDC: 512.542
Language: Russian
Citation: W. Guo, M. R. Zinov'eva, A. S. Kondrat'ev, “Finite groups whose prime graphs do not contain triangles. III”, Sibirsk. Mat. Zh., 64:1 (2023), 65–71; Siberian Math. J., 64:1 (2023), 56–61
Citation in format AMSBIB
\Bibitem{GuoZinKon23}
\by W.~Guo, M.~R.~Zinov'eva, A.~S.~Kondrat'ev
\paper Finite groups whose prime graphs do not contain triangles.~III
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 1
\pages 65--71
\mathnet{http://mi.mathnet.ru/smj7745}
\crossref{https://doi.org/10.33048/smzh.2023.64.106}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 1
\pages 56--61
\crossref{https://doi.org/10.1134/S0037446623010068}
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