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• W2039594013 abstract "For a finite nonabelian group $G$ let $rat(G)$ be the largest ratio of degrees of two nonlinear irreducible characters of $G$. We show that nonabelian composition factors of $G$ are controlled by $rat(G)$ in some sense. Specifically, if $S$ different from the simple linear groups $PSL_2(q)$ is a nonabelian composition factor of $G$, then the order of $S$ and the number of composition factors of $G$ isomorphic to $S$ are both bounded in terms of $rat(G)$. Furthermore, when the groups $PSL_2(q)$ are not composition factors of $G$, we prove that $|G:Oinfty(G)|leq rat(G)^{21}$ where $Oinfty(G)$ denotes the solvable radical of $G$." @default.
• W2039594013 created "2016-06-24" @default.
• W2039594013 creator A5000262859 @default.
• W2039594013 creator A5049260043 @default.
• W2039594013 date "2013-08-05" @default.
• W2039594013 modified "2023-09-23" @default.
• W2039594013 title "Controlling composition factors of a finite group by its character degree ratio" @default.
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