在本项目中，我们将研究几类局部有限单群与局部幂零p-群。对于局部有限单群，我们探讨p-type和1-type这两类局部有限单群的分类及相关问题，并探讨局部有限单群的一个公开问题：是否存在局部有限单群使得它有一个有限子群的中心化子是有限的？而对于局部幂零p-群，我们主要研究局部幂零p-群的幂结构以及局部极大类p-群的结构性质和应用。

In this project, we will study some classes of locally finite simple groups and locally nilpotent p-groups. First, we will focus on the p-type and 1-type locally finite simple groups and an open question: is there a locally finite simple group with a finite subgroup such that its centralizer is finite? Moreover, we will focus on the power struture of some locally nilpotent p-groups and some locally nilpotent p-groups in which every finite subgroup is contained in a finite p-group of maximal class.