Verifying Huppert's Conjecture for 2 G 2(q 2)

Let G be a finite group and cd(G) be the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G a parts per thousand...aEuro parts per thousand HxA, where A is an abelian group. In this paper, we verify the conjecture for the twisted Ree groups (2) G (2)(q (2)) for q (2) = 3(2m + 1), m a parts per thousand yenaEuro parts per thousand 1. The argument involves verifying five steps outlined by Huppert in his arguments establishing his conjecture for many of the nonabelian simple groups.