Exercise 28, § 4

Give an example of a $\mathbf{Z}$-module $M$ such that, for some prime number $p$ such that $(p) \in \operatorname{Supp}(M)$, there exists no $\mathbf{Z}$-homomorphism $\neq 0$ from $M$ to $\mathbf{Z}/p\mathbf{Z}$.