Finite groups with an irreducible character of large degree

Nguyen Ngoc Hung; Mark L. Lewis; Amanda A. Schaeffer Fry

Finite groups with an irreducible character of large degree

Group Theory 2015-05-20 v1

Authors: Nguyen Ngoc Hung , Mark L. Lewis , Amanda A. Schaeffer Fry

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.

Keywords

finite groups irreducible characters character degree group order upper bound

Cite

@article{arxiv.1505.05138,
  title  = {Finite groups with an irreducible character of large degree},
  author = {Nguyen Ngoc Hung and Mark L. Lewis and Amanda A. Schaeffer Fry},
  journal= {arXiv preprint arXiv:1505.05138},
  year   = {2015}
}

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