Homological realization of prescribed abelian groups via $K$-theory
  Using algebraic and topological K-theory together with complex C^*-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and isomorphic to two arbitrarily prescribed abelian groups in dimensions two and three. 
A. J. Berrick and M. Matthey