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 $g=f \circ \alpha$ ?
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 $g=f \circ \alpha$ ?