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We characterize groups with this property in the following classes of groups:\n  (a) bounded precompact abelian groups;\n  (b) minimal abelian groups;\n  (c) totally minimal abelian groups;\n  (d) \\omega-bounded abelian groups.\n  We also provide examples of minimal abelian groups with this property, and show that there exists a minimal pseudocompact abelian group with the same property; furthermore, under Martin's Axiom, the gro","authors_text":"D. 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