2024-12-26【Basic Abstract Algebra】Exercises for Section 3.3 — Homomorphism of groupsFindoutallpossiblehomomorphismfrom\(\mathbbZ_7\to\mathbbZ_{12}\).Solution:Let\(\varphi\)besuchahomomorphism.Since\(\mathbbZ_7\)isacyclicgroup,so\(\varphi\)isspecifiedby\(\varphi(\bar1)\).Since\(o(\bar1)=7