Example of Intersection of Pure Subgroup which is not Pure

I have learnt that the intersection of pure subgroups of a group $G$ is not necessarily pure. Can someone show me an example when such a case exists?

I'm aware that if $G$ is torsion-free, then the intersection of pure subgroup ls of $G$ is necessarily pure. So the example above must involve for which the group $G$ is not torsion-free.

Any idea? Thanks.

edit: The group $G$ here we are talking about is abelian, of course.

This is exercise 10.33(i) in Rotman's "An Introduction to Group Theory". You can take $G=\mathbb Z_2 \times \mathbb Z_8$. Take $A$ the subgroup generated by $(0,1)$ and $B$ the subgroup generated by $(1,1).$ Then $A$ and $B$ are pure, but their intersection will be the subgroup generated by $(0,2)$, which is not pure in $G$.