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| ≤ e 4−e 3 whenever e > 1. This bound is best possible and improves on several earlier related results.
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Nguyen N. Hung is partially supported by the NSA Young Investigator Grant #H98230-14-1-0293 and a Faculty Scholarship Award from the Buchtel College of Arts and Sciences, The University of Akron.
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Hung, N.N., Lewis, M.L. & Schaeffer Fry, A.A. Finite groups with an irreducible character of large degree. manuscripta math. 149, 523–546 (2016). https://doi.org/10.1007/s00229-015-0793-z
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DOI: https://doi.org/10.1007/s00229-015-0793-z