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On degrees of irreducible Brauer characters

Author: W. Willems
Journal: Trans. Amer. Math. Soc. 357 (2005), 2379-2387
MSC (2000): Primary 20C20, 20G40
Published electronically: September 2, 2004
MathSciNet review: 2140443
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Abstract: Based on a large amount of examples, which we have checked so far, we conjecture that $\vert G\vert _{p'}\le\sum_\varphi \varphi(1)^2$ 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.

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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
Article copyright: © Copyright 2004 American Mathematical Society

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