On Semi CAP*-Subgroups And Generalized TI-Subgroups Of Finite Groups

In the study of group theory,characterizing the global from the local is a common method.Among them,studying the structure of groups from characteristics of some special subgroups has been the focus of finite group theory research.It is particularly common to study solvable group,p-supersolvable group and p-nilpotent group-as basic and important classes of finite groups,through characteristics of different subgroups Among these subgroups,semi(CAP*-subgroups and TI-subgroups have been studied by some scholars.This dissertation will continue to study the influence of the two classes of subgroups and their generalizations on the solvability,p-supersolvability and p-nilpotency of finite groupsIn Chapter 3,we mainly study the influence of some semi(CAP*-subgroups on the structure finite groups.First,by using the semi CAP*properties of some maximal subgroups,2-maximal subgroups,maximal subgroups of Sylow subgroups,3-maximal subgroups and solvable maximal subgroups or 2-maximal subgroups,we obtain some sufficient or necessary conditions for the solvability of finite groups.Second,we use some semi CAP*-subgroups of p-power order to obtain several sufficient or necessary conditions for a finite group to be p-supersolvable,supersolvable or p-nilpotent,which generalize many related well-known resultsIn Chapter 4,we first generalize TI-subgroups to be CTI-subgroups and PTI-subgroups and respectively give their basic properties.Second,by using QTI-subgroups and CC-subgroups,we obtain several sufficient conditions for the solvability and 2-nilpotency of finite groups.Next,we give an incomplete classification of all finite groups whose maximal subgroups are CTI-subgroups.Finally,we investigate the connection between APTI-groups and modular groups.