i have learn that intersection of pure subgroup 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 intersection of pure subgroup of G are 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.