On the dimension of matrix representations of finitely generated torsion free nilpotent groups

Abstract

It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into GLn(Z) for an appropriate n 2 N; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in (6). In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced as well as provide a modification of the algorithm presented in (6).