有限p群是有限群最基本和最重要的分支之一. 近年来,随着有限单群分类的最终完成, 有限p群的研究才变得越来越活跃.但是有限p群的一般同构分类问题是十分困难的. 这是因为p群的结构相当复杂. 于是在有限p 群的研究领域中,用子群的正规性来研究大群的结构成为重要的研究课题之一。. 本项目研究用子群的正规化子来刻画其正规性，研究正规化子与有限p群的关系以及正规化子与正规闭包之间的联系。首先研究在限定子群正规化子较大的前提下，研究有限p群的性质。然后研究具有较小正规化子的有限p群的结构。最后对正规化子和正规闭包之间的关系做进一步探讨。

Finite p-groups play an important and basic role in the finite group theory. After the classification of finite simple groups is finally completed, the study of finite p-groups becomes more and more active. However, the finite p-groups are so complicated that it is quite difficult to give a complete classification of all non-isomorphic p-groups. So to study p-groups by the normality of the subgroups becomes one of topics in finite p-groups. . In this project, we characterize subgroup' normality by its normalizer and then study the relationship between normalizers and finite p-groups. On the one hand, we study the finite p-groups with large normalizers. On the other hand, we investigate the structure of finite p-groups when the normalizers of some subgroups are small. After the above work, we will do further exploration and research to reveal the intrinsic link between normal closures and normalizers.