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.
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Funding
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).
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 1, pp. 65–71. https://doi.org/10.33048/smzh.2023.64.106
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Guo, W., Zinov’eva, M.R. & Kondrat’ev, A.S. Finite Groups Whose Prime Graphs Do Not Contain Triangles. III. Sib Math J 64, 56–61 (2023). https://doi.org/10.1134/S0037446623010068
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DOI: https://doi.org/10.1134/S0037446623010068