Generalized dimension subgroups and derived functors

Every two-sided ideal $\mathfrak{a}$ in the integral group ring $\mathbb{Z}[G]$ of a group $G$ determines a normal subgroup $G\cap (1+\mathfrak{a})$ of $G$. In this paper certain problems related to the identification of such subgroups, and their relationship with derived functors in the sense of Dold-Puppe, are discussed.