The P-center Automorphism Of Finite Groups And Their Applications

The set of p-central automorphisms of a finite group is a meaningful research object in group theory.It is not only related to the study of Coleman automorphisms of finite groups,but also closely related to the study of units of integral group rings(especially the normalizer problem).In this paper,p-central automorphisms of some classes of groups will be further studied.In chapters 2 and 3,we study p-central automorphisms of primitive groups and critical groups respectively,and prove that there exits certain prime factor p of || G such that every p-central automorphism of G is inner.As a direct corollary,the normalizer property holds for both primitive groups and critical groups.The holomorph of a group is the semi-direct product of the group and its automorphism group.As applications of the above results,we study Coleman automorphisms of the holomorphs of primitive groups and critical groups in chapters 2and 3 respectively,and prove that every Coleman automorphism of these holomorphs is inner.