The character degree ratio and composition factors of a finite group

Abstract

For a finite non-abelian group $G$ let $\rat(G)$ denote the largest ratio of degrees of two nonlinear irreducible characters of $G$. We prove that the number of non-abelian composition factors of $G$ is bounded above by $1.8\ln(\rat(G))+1.3$.

To appear in Monatshefte fur Mathematik