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Does there exist a short exact sequence of the form $$0\to \mathbf Z\to \mathbf Z\oplus (\mathbf Z/n\mathbf Z) \to \mathbf Z/n\mathbf Z\to 0$$ which does not split?

(Note: Don Alejo provided a link which answered part of my earlier question, which merely asked for the existence of a non-split exact sequence of the form $0\to A\to A\oplus C\to C\to 0$.)

user26857
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caffeinemachine
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  • This question has been asked several times here, see e.g. http://math.stackexchange.com/questions/1980432/ I think for finitely generated abelian groups, such a counterexample does not exist. –  Apr 08 '17 at 16:14
  • When I've closed this as a duplicate of http://math.stackexchange.com/questions/135444/a-nonsplit-short-exact-sequence-of-abelian-groups-with-b-cong-a-oplus-c I've read that thread (while those who voted for reopening and the OP certainly don't) and found two answers which prove that such a sequence can't exist. – user26857 Apr 08 '17 at 20:15
  • @user26857 I apologize for not noticing the relevant answers. Is it possible that you mark this as a duplicate again? Thanks. – caffeinemachine Apr 08 '17 at 20:41

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