众所周知，p-群和单群是决定有限群结构的两个“基本的”群结构。1982年单群分类完成以后，单群本身的结构、p-群的结构、单群在决定有限群结构中如何发挥作用是三个值得研究的问题。本项目将以单群分类定理作为依据给出三种刻画有限群结构的方法（特殊共轭类长度与群结构，不可约特征标维数和个数对有限群结构的影响，高阶元的阶、2-Sylow子群阶或群的阶对群的结构的影响）、研究Shult猜想；在p-群结构方面，研究极大类p-群的推广及两个公开问题。

It is well-known that p-groups and simple groups are two "fundamental" group structure to construct finite groups. After the completion of classification of finite simple groups in 1982, there are three topics worth to be studied: to find out all structure information of simple groups, to find out all structure information of p-groups, and to study structure of finite groups by its simple sections. In this project, we use the Classification Theorem of Finite Simple Groups and three kinds of information to character finite groups: special lengths, degrees and numbers of irreducible characters, large element orders and order of 2-Sylow subgroup or order of a group, Shult's conjecture. On the structure of p-groups we study the generalizations of p-groups of maximal class and two open problems.