幂自同构建立了子群的正规性与自同构之间的联系，本项目就是围绕某些特殊子群上诱导的幂自同构来展开的，运用临界群的思想，利用局部分析的方法，通过群系剩余的正规化子，数量性质及自同构导子来寻求有限群结构的刻画，这也为这方面的研究提供新的想法和途径。..本项目主要从三个方面展开，一. 探究广义 norm 与广义 Wielandt 子群，深入研究每个子群的幂零剩余都正规的有限群，二. 寻找有限群的F-剩余与F-中心之间的数量关系，三. 研究特殊子群的自同构导子是大或小的有限群。

Power automorphisms establish a nice link between the normality of subgroups and automorphisms, this project, around the power automorphism induced by some special subgroup, is aim to characterize the structure of finite group by applying the idea of critical group and the method of local analysis, though the normalizers, Quantities and automizers of the formational residuals, it also provides new ideas and approaches to the research in this area...The project is mainly divide into three aspects, on one hand, investigate the generalized norm and Wielandt subgroup，go deep into the class of finite group that every nilpotent residual of subgroup is normal, on the other hand, look for the relationship of size between the F-residual and F-center in finite groups, finally, study the finite group with small or large automizers of some special subgroup.