The Influence Of Some Special Subgroups On The Structure Of Finite Groups

In the theory of finite groups, people usually use some propertiesof subgroups to study the structure of finite groups. For instance, one mayobtain the suffcient condition for a finite group to be solvable by using theC-Normality of maximal subgroup. In this paper, we firstly use the weakC-Normality of minimal subgroup, the maximal(second maximal)subgroupsof Sylow subgroup to study the suffcient condition for a finite group to bep-nilpotent; secondly, we use the S-Normality of maximal subgroups, themaximal(second maximal)subgroups of Sylow subgroup to study the suffcientcondition for a finite group to be solvable or p-nilpotent; at last,on the basisof the theory of formations, we use the C-supplementy of some subgroups andF-supercenter, some sufcient conditions of a finite p-nilpotent or supersolvablegroup and generalized results of Ito Theorem are proved. Some results in thispaper also generalize some known ones.