关于子群σ-性质与有限群的结构以及p-群的一些问题研究

本项目将主要从事与σ-群理论相关的一些新的课题研究。我们将研究子群的一些σ-性质与有限群的结构以及有限p-群中的一些问题。其主要研究内容包含以下5个研究课题：1）利用子群的弱m-H-置换性和相关嵌入性研究有限群的结构；2）研究子群的sσ-拟正规可迁性与有限群的结构；3）利用两种子群格来研究有限群的结构；4）研究新的广义norm子群与有限群的结构；5）所有内交换子群的阶均为p³的有限p-群结构的进一步研究。本项目所有课题都跟国际潮流接轨，处于该领域的研究前沿，其成果对丰富群的理论和促进相关学科的发展具有重要意义。

This project will be mainly engaged in the research of some new topics related to the theory of σ-groups. We will study some problems on some σ-properties of subgroups and structures of finite groups and finite p-groups. The project includes 5 research topics: 1) study the structure of finite groups by using weakly m-H-permutability and embeddedness of subgroups; 2) study the structure of finite groups in which sσ-quasinormality is a transitive relation; 3) study the structure of finite groups using two subgroup lattices; 4) study the influence of some new generalized norm and Wielandt subgroups on the structure of finite groups; 5) further study the structure of finite p-groups all of whose minimal nonabelian subgroups are of order p³. All subjects are the academic front, and some of them have original ideas. The research results are of great significance for enriching the theory of groups and promoting the development of related disciplines.