Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups

Resumo

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.