Finite Groups With Some CSS-Subgroups Of Prime Power Order

For a long time,studying the influence of generalized normal property of some subgroups of prime power order on the structure of a finite group has been widely concerned.In this paper,we start from“the certain normal property”of subgroups with order p~mand some maximal subgroups of Sylow subgroups of a finite group to reveal the internal relations between it and the p-nilpotency of a finite group.The results obtained generalize some existing results.There are four chapters in this dissertation.In Chapter 1,we introduce the background of this dissertation and list some main results.In Chapter 2,we give some basic concepts and common conclusions used in this dissertation.In Chapter 3,we mainly discuss the p-nilpotency of a finite group under the assumption that every subgroup with order p~mof its Sylow subgroups is a CSS-subgroup,and extend some classical results.And give an a rmative answer to some of the questions raised by Heliel and others.In Chapter 4,we characterize the structrue of a finite group whose partial maximal subroups of its Sylow subgroups are CSS-subgroups or S-quasinormally embedded subgroups,and obtain some su cient conditions for a finite group to be p-supersolvable or p-nilpotent.