问题8：为什么有了同构概念，我们还需 要研究同态？ A homomorphism between groups (G,)and (H,o)is a map:GH such that p(g1·g2)=(g1）op(g2) for g1,92EG.The range of o in H is called the homomorphic image of o. 通常情况下，我们对满同态更有兴趣！ Example 1.Let G be a group and gG.Define a map ZG by o(n)=g".Then o is a group homomorphism,since (m+n)=gm+n=g"g”=(m)(n). This homomorphism maps Z onto the cyclic subgroup of G generated by g.问题8：为什么有了同构概念，我们还需 要研究同态？ 通常情况下，我们对满同态更有兴趣！