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A lot of solutions to problems say that for a cyclic group, such as $\mathbb{Z}/\mathbb{Z}_3$, $\mathbb{Z}/\mathbb{Z}_{10}$, etc., a group homomorphism $\phi$ from $\mathbb{Z}/\mathbb{Z}_m$ to $\mathbb{Z}/\mathbb{Z}_n$ is determined by $\phi(1)$, but I never really understood why... can someone help me? Thanks so much in advance!

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