Completely divisibility-closed normal subgroup

Definition
Suppose $$G$$ is a group and $$H$$ is a subgroup of $$G$$. We say that $$H$$ is a completely divisibility-closed normal subgroup of $$G$$ if the following equivalent conditions are satisfied:


 * 1) $$H$$ is both a normal subgroup of $$G$$ and a completely divisibility-closed subgroup of $$G$$.
 * 2) $$H$$ is a normal subgroup of $$G$$, and for any prime number $$p$$ such that $$G$$ is $$p$$-divisible, the quotient group $$G/H$$ is $$p$$-torsion-free.