1.6.73 Fields, Groups, Rings

condition: Let \( \varphi- \) be a non-injective homomorphism of \( \mathbb{Z} / 13 \mathbb{Z} \) and some group \( G \). Prove that \( \varphi(x)=e \) for all \( x \in \mathbb{Z} / 13 \mathbb{Z} \).