Generalized Complementable Subgroups About Localization

Studying the structure of a group is the main content of the research about the Group Theory.Many scholars obtained important results on the structure of groups by using the properties of subgroups to explore finite groups.In this paper,we will restrict the near m-embedability,the Mp-supplementation and the weak M-supplementation of subgroups to the normalizer NG(P)of G,where P is a Sylow p-subgroup of G,and discuss the structure of p-nilpotent groups and p-supersolvable groups by virtue of the near m-embedability of an element of H(P).Meanwhile we will study the construction of the hypercentre by using the weak M-supplementation of subgroups.The paper divides into the following three chapters.Chapter 1,introduction.We will introduce the background about this paper.Chapter 2,basic definition and main lemmas.We will give some basic definitions and main lemmas which will be used in this thesis.Chapter 3,the main conclusions and the proofs in detail.