本项目旨在对影响p群结构的几个基本问题及与之相关的问题开展研究。大量的研究成果表明：内交换子群、基本子群(我们提出的一个新概念)对p群结构有着深刻的影响。 p群的正规结构和幂结构之间的联系和相互作用是p群理论中最深刻的问题。基于这样的观察，本项目通过对内交换子群、基本子群的某种限制考察和刻画p群结构；通过p群的正规结构与算术结构的联系、正规结构与幂结构的联系刻画并分类某些p群。其意义在于：（1）这些问题的研究与结果对p群本身具有重要性，特别是对有限（单）群的研究也具有重要影响；（2）p群为组合、上同调理论以及计算机科学提供了理想的研究对象；（3）p群研究目前在我国还很薄弱，此项目旨在进一步加强该领域的研究，建立稳定的p群研究队伍，形成明显的研究特色，在这个领域中做出中国人的更大贡献。还要指出，在我们的研究中将广泛应用计算群论的软件包Magma，因此对它的开发和应用也是本项目的一个重要特点。

The propose of this project is to invesitigate some basic problems and related problems which influences the structure of finite p-groups. A lot of results shows that the structure of finite p-groups are deeply influenced by minimal nonabelian subgroups and basic subgroups, respectively. It is needed to be pointed that the concept of basic subgroups is introduced by us. The interrelation and interaction between the power structure and the normal structure of p-groups is a profund problem in p-group theory. Basic on such observation, this project investigates the sturcture of p-groups by suitable restriction to minimal nonabelian subgroups and basic subgroups, respectively, and also characterise and classifies some p-groups by the interrelation and interaction between the power structure and the normal structure of p-groups. The significance of this project is: (1) the result is impotant for p-group theory, in particular, for the study of the classification of finite simple groups; (2) the p-groups provides a good research subject for combination, cohomology, computer science. (3) the research to p-groups is weak in China. The project is to sharp the research in p-groups, stable a research team, form a bright style and make more contribution. In addition, we will often use software Magma, to develop and apply deeply Magma is also bright style.