The Influence Of The Projective Limit Properties Of Groups On The Coleman Automorphisms Of Finite Group

The problem of normalizing subconjecture of unit group in integral group ring of finite group can be transformed into the problem of automorphism of the finite group.Coleman automorphism group,as a subgroup of automorphism group,has profound significance to the study of the structure of the group.In recent years,with the development of normalizers in integral rings,Coleman automorphism has become one of the hot topics in the theory of finite integral rings.According to the projective limit property that any finite group can be expressed as some factor groups,this thesis investigates the influence on the automorphism of the finite group.Firstly,we construct a Coleman automorphism method for solvable finite groups.Secondly,we calculate the Coleman automorphism of some subcyclic groups and subabelian groups,obtain the concrete structures of the Coleman automorphism groups and Coleman outer automorphism groups of these groups,and generalize some famous theorems.