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.
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Translated from Algebra i Logika, Vol. 57, No. 2, pp. 175–196, March-April, 2018.
*Supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant MK-6118.2016.1), by the Complex Research Program of UrO RAN (project No. 18-1-1-17), and by the Program for State Aid of Leading RF Universities (Agreement No. 02.A03.21.0006 between the Ministry of Education and Science of the Russian Federation and the Ural Federal University, 27.08.2013).
**Supported by FAPESP, project No. 2014/08964-1.
***Supported by Dmitry Zimin’s Dynasty Foundation.
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Gorshkov, I.B., Maslova, N.V. Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups. Algebra Logic 57, 115–129 (2018). https://doi.org/10.1007/s10469-018-9484-7
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DOI: https://doi.org/10.1007/s10469-018-9484-7