论文标题
关于威廉姆斯在布劳德角色度上的猜想
On Willems' conjecture on Brauer character degrees
论文作者
论文摘要
2005年，沃尔夫冈·威廉姆斯（Wolfgang Willems）提出了一个猜想，提出了一个有限$ g $的不可约$ p $ brauer字符的平方之和的下限。我们证明了Prime $ P = 2 $的猜想。为此，我们依靠最近将Willems的猜想减少到Tong-Eviet上的准简单群体的问题上。我们还验证了某些有限的准简单群体和奇数素的某些家庭的汤维条件。在途中，我们获得了有限的谎言类型组的常规半圣经共轭类数量的下限。
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.
