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Groups and FieldsEasyHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Easy problem

A homomorphism φ:Z9→Z12\varphi: \mathbb Z_9 \to \mathbb Z_{12} is determined by φ(1)\varphi(1), and 9φ(1)≡09\varphi(1) \equiv 0 in Z12\mathbb Z_{12} must hold. How many homomorphisms φ:Z9→Z12\varphi: \mathbb Z_9 \to \mathbb Z_{12} are there in total?