On degrees of irreducible Brauer characters
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Abstract:
Based on a large amount of examples, which we have checked so far, we conjecture that $|G|_{p’}\le \sum _\varphi \varphi (1)^2$ where $p$ is a prime and the sum runs through the set of irreducible Brauer characters in characteristic $p$ of the finite group $G$. We prove the conjecture simultaneously for $p$-solvable groups and groups of Lie type in the defining characteristic. In non-defining characteristics we give asymptotically an affirmative answer in many cases.References
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Additional Information
- W. Willems
- Affiliation: Institut für Algebra und Geometrie, Fakultät für Mathematik, Otto-von-Guericke-Universität, 39016 Magdeburg, Germany
- Received by editor(s): January 9, 2003
- Received by editor(s) in revised form: October 29, 2003
- Published electronically: September 2, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 2379-2387
- MSC (2000): Primary 20C20, 20G40
- DOI: https://doi.org/10.1090/S0002-9947-04-03561-5
- MathSciNet review: 2140443