Torsion Subgroup Projected Limit And Cluster Rings Of Finite Groups

Based on the existing results in the literature, further research on torsion subgroup of integral group rings theory is carried on in this paper and related results on several aspects are obtained which we state as follows:In chapter1, Torsion subgroup of integral group rings be discussed, the integral group rings is formed by wreath product of cyclic group of order p and q. Some rational conjugate between some subgroups of a infinite integral group rings and its certain subgroup be proved. In the first section of chapter2, we discuss projective limits of groups and its property. In the second section, we expand projective limits of groups into projective limits of the integral group rings. Then we discuss the property of projective limits of the integral group rings. In the third section we discuss the construction of projective limits of the integral group rings. In the forth section, we give a application of projective limits of the integral group rings. We give some conditions that make p-version of the Zassenhaus conjecture hold.