On cancellable Abelian groups

In this paper we show that the additive group Z of integers is cancellable which answers a problem posed in [1] negatively. We also show that every finitely generated abelian group is cancellable. Moreover, we show that a divisible group D is cancellable if and only if the maximal torsion-free subgroup of D is the direct sum of a finite number of copies of the rationals and for each prime p, the p-primary component of D is the direct sum of a finite number of copies of the quasi-cyclic group Z(p∞).