Two Characteristics Of Subgroups And The Structure Of Finite Groups

In this paper, we study the structure of finite groups by using the twocharacteristics of weakly H-subgroups and weaklys*-quasinormally embeddedsubgroups, which mainly involve these problems of p-nilpotency, nilpotency, p-supersolvablitity and supersolvability of finite groups. The paper consists of threechapters. The main content is as follows:In chaper one, we illustrate the background knowledge and the previous researchof weakly H-subgroups and weaklys*-quasinormally embedded subgroups. Welist a lot of basic concepts and important conclusions.In chaper two, we investigate the influence of weakly H–subgroups on thestructure of finite groups. By using the weakly H–subgroups of prime power order,we obtain several criteria on the p-nilpotency and p-supersolvability of finitegroups. Some recent results about H–subgroups are unified and generalized.In chaper three, we firstly define the concept of weaklys*-quasinormallyembedded subgroups and obtain some sufficient conditions about p-nilpotency ofgroups by using its properties.