Embedding Properties Of Subgroups Of P-nilpotent Residual And The Structure Of Finite Groups

Let G be a finite group and H a subgroup of G.Recall that H is S-semipermutable in G if HP=PH for every Sylow p-subgroup P of G with(p,| H|)=1.In the study of the structure of finite groups,it is a very effective method to characterize the structure of finite groups by using the embedding property of subgroups.In this thesis,we mainly discuss p-supersolubility and p-nilpotency of finite groups according to the embedding property of subgroups of p-nilpotent residual,and improve some known results.This thesis includes four chapters.The first chapter mainly introduces the background of group theory and some achievements which are related to this thesis.The second chapter mainly gives the basic concepts and common conclusions.In the third chapter,we mainly use S-semipermutability of subgroups of p-nilpotent residue to study p-supersolubility of finite groups,and obtain some sufficient conditions for p-supersolubility of finite groups,which generalizes some known results.In the fourth chapter,we use Engel condition to give the criterion of p-nilpotency of finite groups,which improves some related results.