Brauer特征标理论是有限群及其表示论中重要而且活跃的分支，此理论中存在许多问题有待解决，它们涉及到不可约Brauer特征标的个数与次数等。本项目拟在这两方面开展工作。..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；在不可约Brauer特征标的次数集合已知的条件下，研究有限群的性质与结构。..通过本项目的研究，Brauer特征标理论将得到一定的丰富。

Brauer character theory is an important and active branch in finite group and its representations. There are many problems in this theory which require solutions and are related to number and degrees of irreducible Brauer characters and so on. We are planning to work on these two topics in this project. ..More specifically, we will characterize structures of finite solvable groups having exactly two nonlinear irreducible Brauer characters , and under the condition that the set of irreducible Brauer character degrees is known, study properties and structures of finite groups. ..Through studies of this project, Brauer character theory would be getting rich.