Spectra of Automorphic Extensions of Finite Simple Exceptional Groups of Lie Type

Abstract

The spectrum ω (G) of a finite group G is the set of orders of elements of G. Let S be a simple exceptional group of type E6 or E7. We describe all finite groups G such that S ≤ G ≤ Aut S and ω (G) = ω (S) and completes the study of the recognition-by-spectrum problem for all simple exceptional groups of Lie type.