Finite Nilpotent Groups By Abelian 2 - Group Circle Plot Normalizer Nature

Among the questions of the integral group ring, the Nomalizer Conjecture is one of the hottest subjects. Although M,Hertweck (2001)constructeded a first counterexample to the normalizer problem. Nevertheless, it is still of interest to find classes of groups for which the normalizer property holds. In this article, we investigate the following two problems.In chapter 2, we investigate the normalizer property of metabelian groups and have the following result:Theorem A Let G be the semidirect product of A and H, where A is an elementary Abelian 2-group and H is an normal Abelian subgroup. Then the normalizer property holds forG.In chapter 3, we investigate the normalizer property for integral group rings of wreath product of finite nilpotent groups by abelian 2-groups, we have the following result:Theorem B Let G= NwrP be the wreath product of N by P, where N is a finite nilpotent group, and P is an abelian 2-group.Then the normalizer property holds forG.