有限群子群的广义正规性与广义可补性的研究

As we known, normal subgroup and complemented subgroup play important roles in the study of finite group. In this project, we will investigate the influence of generalized normality and generalized complementarity of subgroups on the structure of finite groups, and the transitive relation of generalized normality or generalized complementarity of subgroups of finite groups..This project deals with some frontier topics in finite group theory, and its research contents can be divided into three parts as follows:.(1) We will study the influence of generalized normality or generalized complementarity of some subgroups of prime power orders on the structure of finite groups;.(2) We will study the influence of generalized normality or generalized complementarity of all n-maximal subgroups, or some Hall subgroups, or all subgroups on the structure of finite groups;.(3) We will investigate the structure of finite groups in which some generalized normality or generalized complementarity of subgroups is transitive.

我们知道，正规子群和可补子群在有限群的研究中扮演着重要的角色。在本项目中，我们将考察子群的广义正规性和广义可补性对有限群结构的影响，以及有限群子群的广义正规性或广义可补性的传递关系。.本项目涉及若干有限群论的前沿课题，其研究内容可以分为以下三个部分：.（1）我们将研究某些素数幂阶子群的广义正规性或广义可补性对有限群结构的影响；.（2）我们将研究所有n-极大子群，或某些Hall子群，或所有子群的广义正规性或广义可补性对有限群结构的影响；.（3）我们将考察在某种子群的广义正规性或广义可补性传递时有限群的结构。