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Groups with a character of large degree


Author: Noah Snyder
Journal: Proc. Amer. Math. Soc. 136 (2008), 1893-1903
MSC (2000): Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-08-09147-8
Published electronically: February 13, 2008
MathSciNet review: 2383494
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Abstract: Let $ G$ be a finite group of order $ n$ and $ V$ a simple $ \mathbb{C}[G]$-module of dimension $ d$. For some nonnegative number $ e$, we have $ n=d(d+e)$. If $ e$ is small, then the character of $ V$ has unusually large degree. We fix $ e$ and attempt to classify such groups. For $ e \leq 3$ we give a complete classification. For any other fixed $ e$ we show that there are only finitely many examples.

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Additional Information

Noah Snyder
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: nsnyder@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09147-8
Received by editor(s): May 31, 2006
Published electronically: February 13, 2008
Additional Notes: This material is based upon work supported under a National Science Foundation Research Fellowship.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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