Coleman Automorphism And Projection Limit Of Finite Groups

Coleman automorphism began with the study of the normalize problem for the group in the units group of integral group rings.From the point of view for group theory,the Coleman automorphism of finite groups is an inner automorphism problem.In this paper,we focus on two major problems,one is the study of the Coleman automorphisms of finite group,the other is the projective limit.We research the influence of finite psubgroups and their normalizers on Coleman's automorphism by studying the Coleman automorphism of finite groups and the projection limit.At the same time,we introduce the definition and properties of projective limit as well as the application of projective limit of automorphism group.Furthermore,if the group is a projective limit,we could give a complete characterization of the automorphism group.We also use the properties of the projective limit of group to give a concrete construction of the Coleman automorphism group in our paper.As for application,we give some specific examples of groups whose Coleman automorphisms are inner automorphisms,which is of great significance to study of the normalize problem of integral group rings.