Weakly Complemented Subgroups And Finite Group Structure

The theory of finite groups has been a branch of algebra with rich content since the 19th century.In this process,the basic problem of finite groups is studying the structure of finite groups.Many people used properties of various subgroups of finite groups,such as normal subgroups,maximal subgroups,minimal subgroups,Sylow subgroups,the maximal subgroups and minimal subgroups of Sylow subgroups and other subgroups to research the nilpotency,solvability,supersolvability and other structural information of finite groups,and obtained a large number of results.In this thesis,we will weaken the complemented property to weakly supplemented property and study the structure of finite groups.In the third chapter,we use the weakly supplemented property of Sylow subgroups to study the solvability of finite groups and obtain a sufficient and necessary condition for the solvability of finite groups.In chapter 4,we use the maximal and minimal subgroups of the Sylow subgroups to study the p-nilpotenty of finite groups and get some results about saturated formation.The final chapter is some applications of the results in the fourth chapter and some further problems about them.