arXiv 1502.070342015-02-25math.GRmath.RT

The character degree ratio and composition factors of a finite group

Mark L. Lewis, Hung Ngoc Nguyen

备注：: To appear in Monatshefte fur Mathematik

英文摘要：

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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