Generalized Supplemented Subgroups And The Structure Of Finite Groups

It has been very important to study the structure of finite groups by means of the properties of subgroups in the past two decades. In fact, the relationship between the properties of some subgroups and the structure of finite groups has been extensively studied by a number of authors. Since the normality and com-plementarity of subgroups play an important role in group theory, people have generalized them from many aspects. In this paper we shall continue the investi-gation on the influence of some normality and complementarity of subgroups on the structure of finite groups, and get many meaningful new results which extend some known results.Chapter 1 is an introduction of the background of this paper and chapter 2 contain the basic material for later use.In chapter 3 we want to use few complemented minimal subgroups to de-termine the structure of the group using the idea of local analysis. Our results extend not only Hall theorem on complemented groups but also Burnside theorem on p-nilpotent groups.In chapter 4 we introduce the concept of SS-supplemented subgroups, which is a generalization of normal subgroups and complemented subgroups. We obtain some new criterions for p-nilpotency and solvability of finite groups when some subgroups are SS-supplemented.Finally we focus on QTI-subgroups in chapter 5 and obtain a classification of finite groups all of whose second maximal subgroups are QTI-subgroups.