The aim of this article is to draw attention towards various natural but unanswered questions related the lower central series unit group an integral ring.

We calculate the lower Controlled Algebraic K-theory of any nitely generated innnite subgroup of SL(3; Z), the group of 3 3 integral matrices of determinant 1.ally (innnite) cyclic groups.

A free resolution of Z for the integral group ring of the three-dimensional Heisenberg group has been constructed by extending Lyndon’s partial resolution. The integral homology and cohomology have been calculated from there. 3 H AMS Classification: 18G, 20J.