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

DOI: 10.1515/jgth-2022-0119 ISSN: 1433-5883

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

Yong Yang

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.