Some remarks on K₂ of finite group rings and related algebras

In this paper, a study is conducted on K₂ of the group rings with coefficient in Z/pˢZ, where the group is a finite abelian p-group G. The inverse limit of this K₂-group is also considered. Furthermore, for the first part of the study, the case where G is a cyclic p-group is addressed. Moreover, for the second part, the situation where G is a finite abelian p-group is handled. In both cases, an explicit computable isomorphism formula of the corresponding K₂-group is provided, and the results are closely related to the cyclic homology groups.