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The character degree ratio and composition factors of a finite group

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Type
Preprint
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arXiv ID: 1502.07034
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arXiv
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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 $1.8\ln(\rat(G))+1.3$.

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