The Influence Of Some Given Properties Of Second Maximal Subgroups On The Structure Of Groups

Characterizing the structure of groups is the main task of group theory.There are many important methods having been produced in the process of group theory,among which,the use of the characteristics of maximal subgroups and second maximal subgroups to reveal the structure of finite groups has been widely paid attention by many scholars in recent years.We mainly divide the dissertation into two parts.Firstly,we mainly study the distribution of strong and weak second maximal subgroups in p-solvable groups.Secondly,the structure of supersolvable groups and so on is explored by mainly using the generalized cover-avoidance properties of second maximal subgroups.This dissertation is divided into four chapters.Chapter 1,The introduction.The research background and main results related to this dissertation are mainly introduced.Chapter 2,The preliminaries.The basic concepts and lemmas involved in this dissertation are mainly given.Chapter 3,On the strong and weak properties of second maximal subgroups in p-solvable groups.In this chapter,the distribution of strong and weak second maximal subgroups in p-solvable groups is mainly studied by combining with the index of maximal subgroups and second maximal subgroups.Chapter 4,The influence of the generalized cover-avoidance properties of second maximal subgroups on the structure of groups.In this chapter,the influence of the second maximal subgroups with the properties of CAP and CAPu on the structure of solvable chief factors,p-solvable groups and supersolvable groups is mainly investigated.