Finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of solvable groups

TL;DR

This paper classifies all finite almost simple groups that share the same Gruenberg--Kegel graphs as some finite solvable groups, providing a complete characterization of these graph coincidences.

Contribution

It offers a complete classification of finite almost simple groups with Gruenberg--Kegel graphs identical to those of solvable groups, a previously unresolved problem.

Findings

Identified all almost simple groups with matching Gruenberg--Kegel graphs to solvable groups.

Established criteria for when these graphs coincide.

Provided a comprehensive list of such groups.

Abstract

In this paper we describe all the finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of finite solvable groups.