Locally nilpotent endomorphism of an abelian group

Definition
Suppose $$G$$ is an abelian group and $$f$$ is an endomorphism of $$G$$. We say that $$f$$ is locally nilpotent if for every $$x \in G$$, there exists $$n \in \mathbb{N}$$ such that $$f^n(x) = 0$$.