有限群和无限群的结构和性质的若干问题以及群在图论中一些应用

本项目研究有限群、无限群以及图论中14个内容极其丰富的前沿课题：1）两个正规超可解群的积为极小非超可解的群的结构；2）P_{\pi}群类的性质及其相关问题；3）单连通线性代数群和李型群中的两个问题；4）广义置换子群和广义嵌入子群与群的结构；5）群的自同构、极大子群对和群的主群列与群的结构；6）子群性质具有传递性的群的研究；7）具有给定Spencer高的有限群的结构；8）撰写并出版一部新的群论专著；9）无限群的根性研究；10）无限群中两个根群类的积；11）无限群的正规子群结构的研究；12）广义正交图的自同构群；13）对映拟距离可迁图的分类；14）其他课题的研究。所有这些课题跟国际潮流接轨，处于该领域的研究前沿。其中一些研究具有非常重要的创新。本项目将研究解决若干个相关的疑难问题（包括一些公开问题），其成果对于群论及其相关学科的发展具有十分重要的意义。

This project includes 14 subprojects related to finite groups，infinite groups and graphs: 1) The structure of the minimal non-supersoluble group which is a product of two normal supersoluble groups; 2) The properties of the class P_{\pi} of groups and related questions; 3) Two problems in simple connected linear algebraic group and in groups of Lie type; 4) The structure of the finite groups with generalized permutable and generalized embedding subgroups; 5) The autumorphism of groups, maximal subgroup pairs, chief series of groups and the structure of groups; 6) The research of the groups in which some properties of subgroups is a transitive relation; 7) The structure of the finite groups with given Spencer height; 8) To write a new monograph (book) of group theory; 9) The research of radical theory for infinite groups; 10) The product of two radical classes of infinite groups; 11) The structure of the normal subgroups of infinite group; 12) The automorphisms of generalized orthogonal graphs; 13) To classify antipodal near distance transitive graphs; 14) To study other related problems. All the subjects are on the academic front, and some of them have original ideas. We will solve a series of problems (containing some open problems). The results are significant for group theory and related fields.