Huppert's Conjecture for finite simple exceptional groups of Lie type

TL;DR

This paper proves that any finite group with the same set of complex irreducible character degrees as a finite simple exceptional group of Lie type must be isomorphic to that group times an abelian group, confirming Huppert's Conjecture for these groups.

Contribution

It verifies Huppert's Conjecture for all finite simple exceptional groups of Lie type, showing their character degree sets uniquely determine the group up to abelian factors.

Findings

Character degree sets determine the group up to abelian factors.

Huppert's Conjecture holds for all finite simple exceptional groups of Lie type.

The result completes the classification for these groups.

Abstract

Let $G$ be a finite group and let $\textrm{cd}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we show that if $\textrm{cd}(G)=\textrm{cd}(H),$ where $H$ is a finite simple exceptional group of Lie type, then $G\cong H\times A,$ where $A$ is an abelian group. This completes the verification of Huppert's Conjecture for all finite simple exceptional groups of Lie type.