Completely divisibility-closed subgroup

Definition
Suppose $$G$$ is a group. A subgroup $$H$$ of $$G$$ is termed completely divisibility-closed if the following holds: for any prime number $$p$$ such that $$G$$ is $$p$$-divisible, and any $$g \in H$$, all $$p^{th}$$ roots of $$g$$ in $$G$$ lie inside $$H$$.