About Product Of Conjugate Classes And Cluster Ring The Automorphism Group Of Some Of The Results

Based on the existing references, we make use of the related group theory knowledge, numerical theory and combinatory method; the following problems are investigated in this paper.In chapter 1, we give some basic definitions and some related theorems which we will be used in this article. In chapter 2, we give the method of how to calculate the conjugate class of a wreath product and the reasons are given. To stress the applications of the wreath product, we give a special wreath product K4wrS3 which is formed by Klein group K4 and symmetric group S3. And in chapter 3, we bat the conjugate class of the wreath product K4wrS3In the last chapter, we discuss the other important problem, on the automorphism group of the integral group ring, we know that G. L. Peterson has proved that the finite group G is a E.R. group when the order of its commutator subgroup is a prime number, so we extend the result and prove that finite p-group G with cyclic commutator subgroup is a E.R. group.