本项目一方面通过研究群的子群性质与群结构之间的联系,给出新的方法，由此来确定群的结构，其研究内容包括：1）研究QF-可补充子群与群的结构；2）研究子群的置换性（置换嵌入性）对群结构的影响；3）描写一类具有特殊子群结构的群的结构（即这个群的每个子群可以表示成素数幂指数的子群的交）。 另一方面，我们研究Fitting类中的两个著名问题，具体内容包括：4）Lockett猜想在一般群类中成立的条件；5）研究并给出《群论中未解决的问题》11.25（a）的一般性回答。

In this program, on the one hand, we study the structures of groups by new technologies, which are obtained through studying the relationship between properties of subgroups and structures of groups. Concretely，it includes the following three aspects: 1) QF-supplemented subgroups and structures of groups; 2) Influence of permutable properties (permutable embedded properties) of subgroups on structures of groups; 3) Study the structure of group G which has special subgroup structure (each subgroup can be written as an intersection of subgroups with prime power indexes). On the other hand, we study two famous problems in Fitting class: 4) Try to give the conditions for Lockett conjecture in general class of groups; 5) Study problem 11.25 in <<Unsolved problems in groups theory>> and try to give a new and more general answer to this problem.