It is well-known that low-dimensional group homology provides a useful tool for studying lower central series, dimension subgroups and augmentation powers of group rings. The aim of this paper is to extend these methods to the study of transfinite augmentation powers and, more generally, to the study of two-sided ideals in group rings and the normal subgroups determined by them. The authors generalize the notion of polynomial 2-cocycles and use a homological approach to the identification of normal subgroups, determined by two-sided ideals of the group rings \(RG\), where \(R\) is the ring of integers or the field of rational numbers. In particular, they investigate transfinite dimension subgroups, determined by the transfinite powers of the augmentation ideals in \(RG\).