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

In the history of finite groups,many scholars have studied the structure of finite groups in virtue of the properties of subgroups,and obtained abundant research results.As the most basic class of subgroups of finite groups,the structure of subgroups of prime power order have a great influence on the structure of finite groups.In addition,as the generalization of the normality of subgroups,TI-subgroups and K-P-subnormal subgroups have an important influence on the structure of finite groups.In this dissertation,on the one hand,we research the influence of strong permutability,strong p-permutability,abnormality and self normality of subgroups of prime power order on the structure of finite groups.On the other hand,we study the structure of finite groups in which some subgroups are TI-subgroups or K-P-subnormal subgroups.In chapter 3,firstly,we research the influence of the self normality or strong permutability of Sylow subgroups on the structure of finite groups in saturated formation,and give the relationship between the self normality or strong permutability of Sylow subgroups and the structure of G;Secondly,we study the structure of when G? (?)?w(?) and every Sylow subgroup of G is (?)-abnormal or strongly permuteral in G;Furthermore,we research the influence of the self normality or strong permutability of Sylow subgroups on the structure of G when G is a metanilpotent group and G?(?)?(?).Finally,we apply the concept of strong p-permutability to research the influence of strong p-permutability or abnormality of Sylow subgroups and their maximal subgroups on the structure of G.In chapter 4,we apply the concepts of TI-subgroups and K-P-subnormal subgroups to research the structure of G in which the nonabelian self-centralizing subgroups are TI-subgroups or K-P-subnormal subgroups.Moreover,we investigate the structure of in which all subgroups of non-prime-power order are TI-subgroups or K-P-subnormal subgroups.Finally,we study the structure of G in which the even order subgroups with order greater than 2 of G are TI-subgroups or subnormal subgroups.And we research the structure of G in which the even order non-metacyclic subgroups with order greater than2 of G are TI-subgroups or subnormal subgroups.In chapter 5,we apply the concept of normal closure and P-subnormal to study the structure of finite groups in which cyclic subgroups of prime power order are P-subnormal in their normal closure.Furthermore,we study the structure of finite groups in which subgroups of prime power order are P-subnormal in their normal closure.