# Explicit indecomposable monomorphism of finitely generated non-indecomposable Abelian groups.

This question is a follow-up of the question I asked here.

Can you write down an explicit example of a monomorphism of finitely generated Abelian groups which is an indecomposable object in the category of two-step complexes of Abelian groups such that one of the two entries is not an indecomposable Abelian group?

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How about the map $f:\mathbb{Z}\to\mathbb{Z}\oplus(\mathbb{Z}/2\mathbb{Z})$ given by $f(n)=(2n,n)$?
Or for a finite example, the same idea works with a map $\mathbb{Z}/4\mathbb{Z}\to(\mathbb{Z}/8\mathbb{Z})\oplus(\mathbb{Z}/2\mathbb{Z})$.
Or if you want neither term to be indecomposable, the map $(m,n)\mapsto(2m,m+2n,n)$ from $(\mathbb{Z}/16\mathbb{Z})\oplus(\mathbb{Z}/4\mathbb{Z})$ to $(\mathbb{Z}/32\mathbb{Z})\oplus({\mathbb{Z}/8\mathbb{Z}})\oplus(\mathbb{Z}/2\mathbb{Z})$.