In mathematics, a slender group is a torsion-free abelian group that is "small" in a sense that is made precise in the definition below.
A torsion-free abelian group G is said to be slender if every homomorphism from ZN into G maps all but finitely many of the en to the identity element.
Every free abelian group is slender.
The additive group of rational numbers Q is not slender: any mapping of the en into Q extends to a homomorphism from the free subgroup generated by the en, and as Q is injective this homomorphism extends over the whole of ZN.
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