I know that any homomorphism will take the identity of the first group to the identity of the second; So assuming that $f$ is a function that takes $Z\_{50} \to Z$ by any homomorphism of groups, I'm curious as to how to show that $f(1) = 0$ ?

I am struggling to see the connections from the finite group of $Z\_{50}$ to the infinite group of $Z$ and how the function mapping would look..

I'm kinda a newbie so any and all help is appreciated