The Influence Of The Localized Nature Of The Embedding On The Group Structure

In this dissertation,studying the relationship between the properties of subgroups and the structure of groups is the main content of the research about the Group Theory.In the process of this study,we obtained the characterization of the structure of a finite group,especially,investigated the saturated formation and the structure of generalized hypercentre of finite groups,and obtained some important results.In this paper,we mainly do the work of the two parts.First,we use the Mp-embedded properties of some subgroups with fixed order in the normalizer NG(P)of G,where P is a Sylow subgroup of G and combines the nearly m-embedded properties of H-subgroups to obtain some results about p-nilpotency and p-superso-lvability of finite groups.Second,considering the nearly M-supplemented properties of primary subgroups,some results about the structure of generalized hypercentre properties are obtained.The paper divides into the following three parts.Part 1,introduction.We will introduce the background about this paper.Part 2,basic definitions and main lemmas.We will give some basic definitions and main lemmas which will be used in this thesis.Part 3,the main conclusions and the proofs in detail.