Divisibility-closed subgroup of abelian group

Definition
A subgroup $$H$$ of a group $$G$$ is termed a divisibility-closed subgroup of abelian group if $$G$$ is an abelian group and $$H$$ is a divisibility-closed subgroup of $$G$$, i.e., for any prime number $$p$$ such that $$G$$ is a $$p$$-divisible group, we have that $$H$$ is also a $$p$$-divisible group.