Verbal subgroup of abelian group

Definition
Suppose $$G$$ is an abelian group and $$H$$ is a subgroup of $$G$$. We say that $$H$$ is a verbal subgroup of abelian group if it satisfies the following equivalent conditions:


 * 1) $$H$$ is a verbal subgroup of $$G$$.
 * 2) There exists an integer $$m$$ such that $$H$$ is precisely the set of $$m^{th}$$ powers in $$G$$.