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Question: is a quotient of a finitely generated torsion free abelian group still torsion free ?

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No, you can consider $2\mathbb Z$ as subgroup of $\mathbb Z$. – Babak Miraftab Apr 16 '13 at 11:34
up vote 0 down vote accepted

Provided that the subgroup you quotient out by is pure, then yes it is.

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