If $$ 1 \rightarrow A \rightarrow E \rightarrow G \rightarrow 1 $$ is an extension of of G by A, and we can find an isomorphic copy of $$G$$ in E, does the sequence automatically split? How would one show that this isomorphism, composed with $$ \pi:E \rightarrow G $$ is the identity on G? Thanks!
2025-01-13 07:56:44.1736755004
Existence of a Section in Group Extension
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