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Suppose we have surjective group morphisms $$f: \mathbb{Z}^n\rightarrow A \qquad g:\mathbb{Z}^n\rightarrow A.$$

How do I construct a group isomorphism $\alpha:\mathbb{Z}^n \rightarrow \mathbb{Z}^n$ such that $g=f \circ \alpha$ ?

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    @Nadori Yikes, I didn't see that you wanted an _isomorphism_. I guess we'll have to be more careful. Is it so clear that you can always do this?2012-02-26
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    You can't: $n=1, A=\mathbb Z/8, g=can, f=3\cdot can$2012-02-26
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    @GeorgesElencwajg I think this is the true "answer" to the question. Very nice!2012-02-26

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