关于Brauer特征标数量性质的研究

We are planning to study the influences of number and degrees of irreducible Brauer characters on finite groups in this project. .More specifically, we will characterize structures of finite solvable groups having exactly two nonlinear irreducible Brauer characters, and study the relations between average value of degrees of irreducible Brauer characters and Willems' conjecture as well as Holm-Willems' conjecture..Through research of this project, Brauer character theory would be getting rich.

本项目拟研究不可约Brauer特征标的个数与次数对有限群的影响。. 具体地，刻画恰有两个非线性不可约Brauer特征标的有限可解群的结构；研究不可约Brauer特征标次数的平均值与Willems猜想以及Holm-Willems猜想的联系。 . 通过本项目的研究，Brauer特征标理论将得到一定的丰富。