Question: Let $G$ and $G^{\prime}$ be two groups and $\phi: G \rightarrow G^{\prime}$ be an onto homomorphism. Let $H=\ker\phi$. Show that $G / H \simeq G^{\prime}.$ Hence show that there does not exist any homomorphism from $Z_{9}$ onto $Z_{6}$.
Progress: I can Show the first part. But I stuck on last part. Can any one suggest me to solve the last part?