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Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)

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edited Jul 16, 2019 at 20:06

Martin Sleziak

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asked May 20, 2014 at 15:37

Felix Y.

Do all exact sequences $0 \rightarrow A \rightarrow A \oplus B \rightarrow B \rightarrow 0$ split for finitely generated abelian groups?

Suppose $A$ and $B$ are finitely generated Abelian groups. Are all exact sequences of the form $0 \rightarrow A \rightarrow A \oplus B \rightarrow B \rightarrow 0$ split?

If not, is there an example?

gr.group-theory abstract-algebra abelian-groups short-exact-sequences