有限可解群是群论中一个非常活跃的研究分支。有限群G被称为是n-维可解的，如果G的主因子的阶数整除某素数的n次方幂，且G至少有一个主因子的阶数等于某素数的n次方幂，其中n为固定的正整数。一个群被称为是双循环群，如果该群可以分解成两个具有平凡交的循环群的乘积。本项目的研究主要集中以下几个方面：.（1）研究低维数的n-维可解群的结构性质，比如，阶数不含5次方因子的有限可解群等；.（2）刻画"较小阶"双循环群，给出该群合适的分解并给出该群的自同构群；.（3）讨论以上结果在"二部图在曲面上的边传递嵌入问题"上的应用。.此外，本项目也将研究对角子群对有限群结构的影响。

Finite solube group theory is a very active branch of group theory. A finite group G is call n-dimensional if the order of each chief factor of G divides n-th power of some prime number, and G has at least one chief factor whose order equals n-th power of some prime number, where n is a fixed natural number. A group is called bi-cyclic if it can be decomposed as a product of two cyclic subgroups with trivial intersection. This project aims to study the following .topics:..(1) Study n-dimensinal soluble groups for small values of n, say the soluble groups whose orders are indivisible by fifth power of any prime;.(2) Characterize the "small-ordered " bicyclic groups,try to give a suitable decompostion for these groups, and try to compute the automorphism groups of these groups..(3) Try to apply the above resuts to the study of edge transitive embedding of bi-partite graphs on the surfaces...In this project, we also study the influence of the diagonal subgroups on the structure of finite groups.