"Inverse" homomorphism of a group monomorphism – math.stackexchange.com

"Inverse" homomorphism of a group monomorphism – math.stackexchange.com

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Assume $\varphi:H\rightarrow G$ is a finite group monomorphism. Is it true that there exists a homomorphism $$ \psi:G\rightarrow H $$ such that $$ \psi\circ\varphi=id_H? $$

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