Geodesic
Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups
Algebra i logika, Tome 57 (2018) no. 2, pp. 175-196

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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, almost simple group, Gruenberg–Kegel graph (prime graph).
Mots-clés : solvable group 
@article{AL_2018_57_2_a2,
     author = {I. B. Gorshkov and N. V. Maslova},
     title = {Finite almost simple groups whose {Gruenberg{\textendash}Kegel} graphs coincide with {Gruenberg{\textendash}Kegel} graphs of solvable groups},
     journal = {Algebra i logika},
     pages = {175--196},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_2_a2/}
}
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I. B. Gorshkov; N. V. Maslova. Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups. Algebra i logika, Tome 57 (2018) no. 2, pp. 175-196. http://geodesic.mathdoc.fr/item/AL_2018_57_2_a2/