The Simple Ree groups ${}^2F_4(q^2)$ are determined by the set of their character degrees

Details The Simple Ree groups ${}^2F_4(q^2)$ are determined by the set of their character degrees The Simple Ree groups ${}^2F_4(q^2)$ are determined by the set of their character degrees

2011-03-21

arxiv.org/abs/1103.3937v2

Mathematics

Group Theory

14 pages, to appear in Journal of Algebra

Scientific paper

10.1016/j.jalgebra.2011.04.034

Let $G$ be a finite group. Let ${\rm{cd}}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we will show that if ${\rm{cd}}(G)={\rm{cd}}(H),$ where $H$ is the simple Ree group ${}^2F_4(q^2),q^2\geq 8,$ then $G\cong H\times A,$ where $A$ is an abelian group. This verifies Huppert's Conjecture for the simple Ree groups ${}^2F_4(q^2)$ when $q^2\geq 8.$

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