Huppert's conjecture on groups determined by character degrees

Let $G$ be a finite group, and let $H$ be a finite non-abelian simple group. Denote by the character degrees of a group the degrees of its complex irreducible characters. Huppert's conjecture. If the sets of character degrees of $G$ and $H$ are the same, then

$$G \cong H \times A,$$

where $A$ is an abelian group. The conjecture asserts that non-abelian simple groups are essentially characterized by their sets of character degrees. The paper proves this conjecture for the almost simple groups with socle a small Ree group considered here, rather than resolving it in full generality.