A characterization of the simple Ree groups 2𝐹4(𝑞2) by their character codegrees

Abstract

Abstract The codegree of a character 𝜒 of a finite group 𝐺 is cod ⁡ ( χ ) := | G : ker ⁡ ( χ ) | χ ⁢ ( 1 ) . \operatorname{cod}(\chi):=\frac{\lvert G:\ker(\chi)\rvert}{\chi(1)}. We show that the set of codegrees of the Ree groups F 4 2 ⁢ ( q 2 ) {}^{2}F_{4}(q^{2}) ( q 2 = 2 2 ⁢ n + 1 q^{2}=2^{2n+1} , n ≥ 1 n\geq 1 ) determines the groups up to isomorphism.