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ISSN 1088-6850(e) ISSN 0002-9947(p)

On degrees of irreducible Brauer characters

Author(s): W. Willems
Journal: Trans. Amer. Math. Soc. 357 (2005), 2379-2387.
MSC (2000): Primary 20C20, 20G40
Posted: 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 is a prime and the sum runs through the set of irreducible Brauer characters in characteristic of the finite group . We prove the conjecture simultaneously for -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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