Study On Generalized Normal Subgroups Of Finite Groups

In this paper, we study the structure of finite groups by using the characteristics of weakly s ? supplemented embedded subgroups, weakly s ? permutable embedded subgroups,weakly s ? permutable subgroups and c ? quasinormal subgroups, which mainly involve these problems of p-nilpotency, nilpotency and solvability important issues. The full text is divided into five chapters. The main content is as follows:In the chapter one, we introduction the background knowledge and the significance research of the paper. Some definitions and results are also mentioned.The second chapter, by using the concept of weakly s ? supplemented embedded subgroups research on the structure of finite groups. Some recent results about weakly s ? permutable embedded subgroups are unified and generalized.Chapter three,we study the influence of weakly s ? permutable embedded subgroups about the structure of finite groups and obtain the sufficient condition in which a group belongs to a given formation.In the chapter four,using the structure of weakly s ? permutable subgroups on the structure of finite groups and get nilpotency, supersolvable several sufficient conditions.In the chapter five,we firstly define the concept of c ? quasinormal subgroups and acquire some sufficient conditions about solvability groups by using its properties.