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arXiv · 1505.05138

Finite groups with an irreducible character of large degree

Nguyen Ngoc Hung·Mark L. Lewis·Amanda A. Schaeffer Fry
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Abstract

Let $G$ be a finite group and $d$ the degree of a complex irreducible character of $G$, then write $|G|=d(d+e)$ where $e$ is a nonnegative integer. We prove that $|G|\leq e^4-e^3$ whenever $e>1$. This bound is best possible and improves on several earlier related results.

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Nguyen Ngoc Hung, Mark L. Lewis, Amanda A. Schaeffer Fry. 2015-05-19. Finite groups with an irreducible character of large degree. https://arxiv.org/abs/1505.05138

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