On Huppert's conjecture for $F_4(2)$

Abstract

Let $G$ be a finite group and let $text{cd}(G)$ be the set of all‎ ‎complex irreducible character degrees of $G$‎. ‎B‎. ‎Huppert conjectured‎ ‎that if $H$ is a finite nonabelian simple group such that‎ ‎$text{cd}(G) =text{cd}(H)$‎, ‎then $Gcong H times A$‎, ‎where $A$ is‎ ‎an abelian group‎. ‎In this paper‎, ‎we verify the conjecture for‎ ‎${F_4(2)}.$‎