Abstract
An abelian group N with discrete topology is called cancellable if for any two abelian topological groups G and H, the product group G×N is topologically isomorphic to H×N if and only if G and H are topologically isomorphic.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∞).
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