Character Stabilizer Limits Of A SBPC-related Nilpotent Subgroup

The representation of finite groups is an important branch of mordern mathematics.Character theory is one of the main tools of the represen-tation of finite groups over the complex field.Isaacs put forward charac-ter stabilizer limits conception when he studied character theory of finite goups.Using the concepts of inductor of a character triple,stabilizer lim-its,and quasi-primitive character triple,Isaacs proved in his article[2],that all N-relative stabilizer limits of irrecducible characters of G have equal degrees,if N is a normal nilpotent subgroup of G.After giving these concepts,we discuss another special kind of goup,that is SPBC-related nilpotent subgroup,and prove that,the stabilizer limits of irrecducible characters of G relative to a SPBC-related nilpotent subgroup also have equal degree.This academic dissertation is divided into three chapters altogether.In chapter one,we introduce the groundwork of this text,also the research direction and the trends of the development.In chapter two,we give some fundamental conceptions and important results related to the thesis.This can provide necessary preparation for the next chapter.In chapter three,first we difine a new kind group,that is SBPC-related nilpotent subgroup,and give an example to show this kind of group is existential.Thus the discussion of this paper is sensible;second,using con-cept of primitive character triple,we discuss the relationship between the character stabilizer limits of a normal SBPC-related nilpotent subgroup and quasi-primitive character triple;third,by discussing the quasi-primitive character triple,we show the relationship between the stabilizer limits of a normal SBPC-related nilpotent subgroup.