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For questions on modules over rings.
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A question concerning a short exact sequence with an action
Let $A$ and $D$ be two non-trivial abelian groups and $B,C$ be two non-abelian groups. Also, let $C$ is a free group and acts on $A,B,D$.
Let $0\to A \xrightarrow{f}B\xrightarrow{g}C\to 0$ be a s …