Subgroup realizable as the commutator of the whole group and a subgroup

Definition
A subgroup of a group is termed realizable as the commutator of the whole group and a subgroup if it can be realized as the commutator of the whole group and a subgroup.

Stronger properties

 * Weaker than::Perfect normal subgroup
 * Member of the (finite) lower central series

Weaker properties

 * Stronger than::Subgroup realizable as the commutator of two subgroups
 * Stronger than::Normal subgroup: