The Influence Of Local Properties Of Subgroups On The Structure Of Finite Groups

For a long time,the relationship between the properties of subgroups and the structure of finite groups is one of the important topics in the study of finite group theory.In this dissertation,we mainly study the structure and properties of finite groups by the local properties of some subgroups,and obtain many new meaningful results.This dissertation is divided into 5 chapters.In Chapters 1 and 2,we present the research background of this dissertation and some concepts and common conclusions needed in this dissertation.In Chapter 3,we mainly study the influence of the SS-supplemented subgroups on the structure of finite groups.We get the sufficient conditions of solvable groups,p-nilpotent groups,supersolvable groups and a specific saturated formation under assuming that some subgroups are SS-supplemented.At the same time,some known results are also promoted.In Chapter 4,we study the relationship between the pronormal subgroups and the structure of finite groups.By assuming that all the maximal subgroups of the Sylow subgroup of a group G satisfy the pronormality in a local subgroup of G,we obtain some criteria about the group being a p-nilpotent group and a supersolvable group,and generalize some previous results.In Chapter 5,we study the influence of the weakly pronomal subgroups on the structure of finite groups.We have some results about p-nilpotent groups and a saturated formation containing all supersolvable groups by discussing the weak pronormalities of some subgroups of order p in the normalizer of Sylow p-subgroups.These results generalize Asaad’s theorem.