Abelian verbal subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed an abelian verbal subgroup if $$H$$ is an abelian group in its own right (i.e., it is an abelian subgroup of $$G$$) and $$H$$ is a verbal subgroup of $$G$$.

Examples

 * In an abelian group, the verbal subgroups are precisely the power subgroups, see verbal subgroup of abelian group.
 * In a nilpotent group, second half of lower central series of nilpotent group comprises abelian groups, so all of these are abelian verbal subgroups.
 * In a solvable group, the penultimate term of the derived series is an abelian verbal subgroup.