The Influence Of Some Embedding Properties Of Subgroups On The Structure Of Finite Groups

In the study of finite group theory,one of the main research contents is to characterize the structure of finite group.At present,using the embedding property of subgroups to study the structure of finite groups has always been a hot topic for scholars,and many meaningful results have been obtained.In the thesis,we study the influence of weakly HC-embedded subgroups and SS-supplemented subgroups on the structure of finite groups.The whole dissertation is divided into four chapters.Chapter 1,we introduce the research background and development status of this thesis.Chapter 2,we introduce some basic concepts and lemmas related to this dissertation.Chapter 3,to study the influence of weakly HC-embedded subgroups on the structure of finite groups,the p-supersolvability and p-nilpotency of finite groups are described by using the weakly HC-embeddedness of some fixed order subgroups of Sylow subgroups and p-nilpotency of some local subgroups.Chapter 4,to study the influence of SS-supplemented subgroups on the structure of finite groups.Firstly,using 2-minimal and 2-maximal subgroups of Sylow subgroups get A4-free groups are p-nilpotent,respectively;secondly,be-cause 2 is a special prime number,we use SS-supplemented subgroups to give a sufficient condition that the finite groups are 2-nilpotent;then SS-supplemented subgroups are restricted to the local subgroup NG(P)to study the p-nilpotency of finite groups;and next the correlation results of some saturated formations are given;finally,the SS-supplemented group is characterized.