On the Structure of Unitary Units of F3mC9 and F3m(C3 ×C3)

Abstract

In this thesis, we have constructed the group ring matrix of group algebras F3mC9 and F3m(C3 ×C3). We have found center of group algebras F3mC9 and F3m(C3 ×C3). On the basis of group ring matrix, the center of unitary unit group have been established and then order of unitary unit group has been computed. We have also studied the above group algebras for m = 1 computationally using the GAP package LAGUNA. The orders of normalized unit groups, unitary unitary group and unit group has been computed. Moreover, Augmented Ideals of the above group algebras has been studied and we have provided their basis.