Coleman Automorphism Of Subcommutative Groups

The coleman automorphism of finite groups begins with the study of the normalize problem of integral group rings that the problem is transformed into the study of some special(Coleman)automorphisms of finite groups.This paper is based on previous studies and has done the following: Firstly,this paper discusses the Coleman automorphism of a finite characteristic single group extended by a finite abelian group or a finite non-abelian single group,which is shown that under some conditions all Coleman automorphism of this group is an inner automorphism;Secondly,the Coleman automorphism of some metabelian groups are studied,and the properties and conclusions of the Coleman automorphism of the special metabelian groups are given;Finally,as for application,the Coleman automorphisms of dihedral groups and generalized dihedral groups are calculated specifically,which is of great significance to study of the normalize problem of integral group rings.