The Influence Of Weakly Complemented Subgroups On The Structure Of Finite Groups

In the development of finite group theory,it is found that the properties of some special subgroups are closely related to the structure of groups.Many group theorists have studied this problem,especially they used the complementary properties of Sylow subgroups,maximal subgroups and minimal subgroups to characterize the structure of finite groups,which has produced a lot of research results.Later,group theorists weakened the complementary properties of subgroups,and proposed the weakly supplemented properties of subgroups.They used the weakly supplemented properties of subgroups to study the structure of finite groups,and generalized some results of complementary subgroups.In this paper,on the basis of previous research results,we continue to study the structure of finite groups by using the weakly supplemented properties of minimal subgroups.In chapter 3,we study the p-nilpotency and solvability of finite groups by using the weakly supplemented properties of minimal subgroups,and obtain a sufficient and necessary condition that finite groups are -nilpotent groups and a sufficient condition that they are solvable groups.In chapter 4,we mainly study the relationship between the weakly supplemented properties of some minimal subgroups and the saturated groups,and give some necessary and sufficient conditions.Generalizations of some theorems are also given.In chapter5,we give the application of the main theorems and some problems of using the weak supplemented properties of minimal subgroups to study the structure of finite groups.