The Application Of Homology Theory In Coleman Automorphism

On the basis of previous studies,this paper aims to solve the problem when the Coleman outer automorphism group of a semidirect product is trivial.We first give the definition of group action,the definition of Coleman automorphism,the definition of wreath product and some basic results used in the following.We use the structure of wreath product to prove the Coleman outer automorphism group of wreath product of finite nilpotent group by abelian group is trivial;use homology theory we research the Coleman outer automorphism of semidirect product of finite groups.Finally,we prove the Coleman outer automorphism of finite inner nilpotent group is trivial.