The Influence Of S-semipermutable Subgroups And SS-semipermutable Subgroups On The Structure Of Finite Groups

An interesting topic in finite group theory is the study of subgroups with certain embedding properties to investigate the structure of finite groups.There are a lot of interesting results.For example,the famous Glauberman-Thompson theorem and the Frobenius theorem.In this paper,we study the properties and structure of finite groups by reducing the number of S-semipermutable subgroups and SS-semipermutable subgroups,and some interesting results were obtained.In Chapter 3,we firstly study the structure of non-MSS-groups whose all maximal subgroups of even order are MSS-groups.Afterwards,we further study the finite group G whose all 2-maximal subgroups of even order are MS S-gro ups and give a classification of such simple groups.In Chapter 4,we focus to reveal the structure of finite group G by studying its subgroup H of order pe which satisfies the embedding condition that H ∩ L is Ssemipermutable in G,where G/L is p-nilpotent.Further,we gradually reduce the number of considered subgroups to study the structure of finite groups and obtain interesting results.In Chapter 5,we obtain two sufficient conditions for the p-nilpotency of finite groups by discussing partial SS-semipermutable subgroups.