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- Jan 26, 2012

- 995

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**Problem**: Let $0\rightarrow A \xrightarrow{\phi}{} B \xrightarrow{\psi}{} C\rightarrow 0$ be an exact sequence of abelian groups. Let $s^{\prime}:B\rightarrow A$ be a homomorphism such that $s^{\prime}\circ \phi=1_A$. Show that $B\cong A\oplus C$.

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