Verbal subgroup of group of prime power order

Definition
A verbal subgroup of group of prime power order is a subgroup of a group where the whole group is a group of prime power order (i.e., a finite $$p$$-group for some prime number $$p$$) and the subgroup is a verbal subgroup.

Examples

 * The commutator subgroup and all members of the derived series and lower central series are verbal subgroups.
 * The agemo subgroups are all verbal subgroups.
 * Subgroups obtained via a combination of applying agemo and taking commutators are also verbal.

Weaker properties

 * Stronger than::Fully invariant subgroup of group of prime power order
 * Stronger than::Characteristic subgroup of group of prime power order
 * Stronger than::Normal subgroup of group of prime power order