On The Study For Subnormality Of Subgroups In Finite Groups

The thesis focuses on the subnormality of subgroups which is an important property . Besides, we mentioned an experience the content about character theory that the auther have read.The body of the thesis is divided into three chapters.Chapter one, based on H. Wielandt's nonsimplicity criterion for subnormality of subgroupsin finite groups, we present another subnormality criterion in finite solvable groups.Chapter two, we induce the concept of weakly ss-supplemented subgroup. It is a furthergeneralization of weakly s-supplemented subgroup which is introduced in[3] by Alexander N.Skiba. According to the property of weakly ss-supplemented subgroup, we can clarify whethera group is solvable. That is by using the weakly ss-supplemented of Sylow subgroups or maxi-mal subgroups of Sylow subgroups, we get a necessary and su?cient condition and a su?cientcondition for a finite group to be solvable. The proof and the result are interesting.Chapter 3 gives a wholly proceeding and an experience as the auther how to construct acharacter table for non-abelian group whose order is 27.