关于Wielandt猜想、Thompson猜想以及群结构的其它一些疑难问题研究

本项目研究有关有限群结构的13个内容极其丰富的前沿研究课题：1）一个50多年没有解决的Wielandt猜想；2）一个广义的Wielandt猜想；3）一个Wielandt公开问题；4）广义Thompson猜想；5）n-极大子群为σ-次正规的有限群的结构；6）建立σ-超可解群的理论；7）研究一些子群的格性质；8）Skiba的一个公开问题；9）利用某些Hall子群的置换性和嵌入性来研究有限群的结构；10）子群的σ-置换可迁性和广义可补性与群的结构；11）有限群的极大子群的素谱的Manakhov的公开问题；12）非可解群对于其Fitting集F的F-内射子的存在性和共轭性问题；13）其它一些相关的问题。本项目计划解决以上具有重要创新的研究课题。所有课题跟国际潮流接轨，处于该领域的研究前沿。

This project includes 13 subprojects related to structure of finite groups: 1) a more than 50 years did not solved Wielandt conjecture; 2) a generalized Wielandt conjecture; 3) a Wielandt’s open problem; 4) a generalized Thompson conjecture; 5) the structure of finite group in which n- maximal subgroups are б-subnormal; 6) to establish the theory of б-supersolvable groups; 7) the lattice of some subgroups; 8) an open problem of Skiba; 9) the structure of finite groups with some permutable or embedded Hall subgroups; 10) the structure of finite groups in which б-permutability is a transitive relation or some subgroups are generalized supplemented; 11) an open problem of Manakhov on prime spectrum of Maximal Subgroups; 12) on existence and conjugacy of F-injectors for Fitting set of non-solvable groups; 13) some other related problems. We will solve the above innovatory problems. All the subjects are the academic front, and some of them have original ideas.