The Influence Of Boundary Factor Properties Of Some Second Maximal Subgroups On Group Structure

Group is an algebraic system in abstract mathematics,and group theory is an important module in modern mathematics.Solvable groups,non-solvable groups and simple groups are important fields in the research of finite groups.It is well known that composition group series are the basic language for characterizing group structures.The composition factor is the basic element of composition group series,which is essentially a single group.Therefore,any finite group can be regarded as finite extensions of simple groups and simple groups.Subgroups are the basic research objects of finite groups.It is an important trend in group theory to extend the study of solvable groups to general groups by using the classification properties of subgroups.Many experts in group theory have made active explorations and obtained many profound conclusions.For example,the local property of subgroups can be used to induce the classification of maximal subgroups and second maximal subgroups,and reveal the intrinsic laws between them and general groups.It would be a beneficial attempt to characterize some non-solvable groups by giving subgroup properties to second maximal subgroups.In this thesis,we will consider the corresponding set of maximal subgroups from the quantitative characters.Then use the core relation of subgroups to classify second maximal subgroups reasonably.And we describe some non-solvable groups by giving the boundary factor properties of the second maximal subgroups.The main content of the paper is divided into the following four aspects.Chapter 1,The introduction.This chapter mainly gives the research background and significance.Chapter 2,The preliminaries.The basic concepts and lemmas involved in this paper are given.Chapter 3,Main conclusions.In this chapter,we consider the set of non-CAPSp*maximal subgroups,then characterizes the group structure by classifying the corresponding second maximal subgroups and giving the boundary factor properties of subgroups.Chapter 4,Main conclusions.In this chapter,we consider the set of non-cp-normal maximal subgroups,then characterizes the group structure by classifying the corresponding second maximal subgroups and giving the boundary factor properties of subgroups.