The Influence Of The Supplementary Property Of Localization On The Group Structure

Studying the structure of a finite group is the main content of the research about the Group Theory.In the process of this study,the relationship between the properties of subgroups and the structure of groups had been widely studied by many scholars and obtained some important results.In this paper,we mainly do the work of the two parts.First,we use the M p-supplemented properties of some subgroups with fixed order in the normalizer NG(P)of G,where P is a Sylow subgroup of G and combine the nearly m-embe-dded properties of H-subgroups to obtain some results about p-nilpotency and p-supersolvability of finite groups.Second,considering the generalized complemented properties of primary subgroups,some results about the relationships between the generalized complemented properties and solvable groups are obtained.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.