1.6.73 Fields, Groups, Rings

Condition: let \ (\ varphi- \) non-index homomorphism \ (\ mathbb {z} / 13 \ mathbb {z} \) and some group \ (g \). Prove that \ (\ varphi (x) = e \) for all \ (x \ in \ mathbb {z} / 13 \ mathbb {z} \).