The Local Permutability Of Subgroups And The Structure Of Finite Groups

It is well known that the essence of studying a finite solvable group can be revealed by some "embedding properties" of Sylow subgroups in a finite group, and there is close relationships between the " embedding properties" of Sylow sub-groups and the certain " normal property" of a finite group. So Study of Sylow subgroups and its subgroups in a finite group or their certain normal properties in some local subgroups is widespread concerned. However, mostly, people inves-tigate the structure of a finite group using the properties of maximal or minimal subgroups of Sylow subgroups as the complexity of the problems. In this thesis, we try to study the structure by some properties of subgroups with order pm of Sylow subgroups of a finite group. Not only many available results are general-ized, including some famous theorems, but also the essential relationship between the properties of some subgroups and the structure of a finite group is revealed.In Chapter 3, we give some sufficient conditions of p-nilpotency of a fi-nite group whose every subgroup with order pm of a Sylow p-subgroup is a S-quasinormal subgroup and generalize the famous Ito Theorem. In Chapter 4, we discuss the structure of a finite group under the assumption that every subgroup of prime power order of its Sylow subgroups is SS-quasinormal subgroup and ex-tend some classical results, including Buckley Theorem and Srinivasan Theorem. Further, we extend the related results to saturated formations. In Chapter 5, we investigate the influence that every subgroup of prime power order of Sylow subgroups is S-quasinormally embedded subgroup on p-nilpotency and supper-solvability of a finite group and also extend our results to saturated formations. In Chapter 6, we study the influence of some (?)-subgroups of prime power order on the structure of a finite group. In Chapter 7, we define a new class of sub-groups of a finite group, called (?)C-subgroups, and investigate the structure of a finite group with the consideration that every maximal or minimal subgroups of its Sylow subgroups is (?)C-subgroup. Moreover, we discuss the structure and some properties of (?)CN-subgroup (?)C*-subgroup.