课题组将在从群系的观点出发，借助GAP等数学软件的帮助，对一些特殊的有限群的结构进行刻画，研究一些特殊的有限群在自动机理论中的应用。　在一些国内群论研究的热点课题如具有特殊嵌入性质的子群的有限群的结构方面, 课题组将强调从局部化的思想出发进行分类工作; 在研究本课题组处于国内外领先的课题如置换积的因子对群结构的影响、具有特殊子群列的群结构方面的内容时，课题组将继续深入下去，保持优势；在一些国际群论的新动态而国内暂时观注比较少的课题如群与语言的关系等方面, 课题组参于进来, 与国际接轨, 以期占有一席之地.本课题既利用研究者的基础和学术背景着重理论研究,以推进有限群的结构方面的前沿理论研究, 又关注有限群论在其它分支方面的应用,展示出有限群论理论研究的应用价值，所以是一个十分有意义的课题.

By using some mathmaticla softwares, such as the GAP, etc, we will investigate the structures of some special kinds of finite groups in the context of formations, and study the applications of finite groups in the automata theory. In the branch which is the Chinese groups theorists' hotpoints, such as the structure of finite groups having some subgroups with some embedding properties, we want to give the classified results in local version; we will continue to investigate the influence of product factors of subgroups on the structure of whole group and the structure of finite groups with some special subgroups series, in theses branchs we have got some leading results. In the branch that there are less-concerned in China, such as the relation of finite groups and the languages, the application of finite groups in the automata, etc, we will pay more and more energies to them to catch up the development of finite groups in the world..In a word, our project has significance in the theory and application of finite groups.