On degrees of irreducible Brauer characters

Willems, W.

doi:10.1090/S0002-9947-04-03561-5

On degrees of irreducible Brauer characters
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Trans. Amer. Math. Soc. 357 (2005), 2379-2387 Request permission

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.

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