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arXiv · 2012.08765

On Willems' conjecture on Brauer character degrees

Gunter Malle
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Abstract

In 2005 Wolfgang Willems put forward a conjecture proposing a lower bound for the sum of squares of the degrees of the irreducible $p$-Brauer characters of a finite group $G$. We prove this conjecture for the prime $p=2$. For this we rely on the recent reduction of Willems' conjecture to a question on quasi-simple groups by Tong-Viet. We also verify the conditions of Tong-Viet for certain families of finite quasi-simple groups and odd primes. On the way we obtain lower bounds for the number of regular semisimple conjugacy classes in finite groups of Lie type.

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Gunter Malle. 2020-12-16. On Willems' conjecture on Brauer character degrees. https://arxiv.org/abs/2012.08765

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