The Simple Ree groups ${}^2{F}_4(q^2)$ are determined by the set of their character degrees

Abstract

Let $G$ be a finite group. Let $\mathrm{cd}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we will show that if $\mathrm{cd}(G)=\mathrm{cd}(H),$ where $H$ is the simple Ree group ${}^2{F}_4(q^2),q^2\ge 8,$ then $G\cong H\times A,$ where $A$ is an abelian group. This verifies Huppert's Conjecture for the simple Ree groups ${}^2{F}_4(q^2)$ when $q^2\ge 8.$

14 pages, to appear in Journal of Algebra