Some remarks on Schur multiplicator of a group being torsion-free

Let G be a group. Among many other results, it is well known that the Schur multiplicator of G (the second integral homology group of G ) is torsion-free for free Abelian groups of finite rank. We consider here some groups, the multiplicator which is torsion-free. As a simple observation, we find that the multiplicator of a divisible nilpotent group is torsion-free. We also prove that the Schur multiplicator of an upper unitriangular group G of order 4 and also of G / γ 3 ( G ) is torsion-free. Some other examples of groups, the multiplicator which is torsion-free are given.