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This article is cited in 6 scientific papers (total in 6 papers)
Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups
I. B. Gorshkova, N. V. Maslovaab a Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
b El'tsyn Ural Federal University, ul. Mira 19, Yekaterinburg, 620002 Russia
Abstract:
It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain $3$-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no $3$-cocliques.
Keywords:
finite group, solvable group, almost simple group, Gruenberg–Kegel graph (prime graph).
Received: 11.03.2016 Revised: 30.05.2016
Citation:
I. B. Gorshkov, N. V. Maslova, “Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups”, Algebra Logika, 57:2 (2018), 175–196; Algebra and Logic, 57:2 (2018), 115–129
Linking options:
https://www.mathnet.ru/eng/al842 https://www.mathnet.ru/eng/al/v57/i2/p175
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