Subgroup realizable as the commutator of two subgroups

Symbol-free definition
A subgroup of a group is termed realizable as the commutator of two subgroups if there exist two subgroups of the whole group such that the subgroup is the commutator of those two subgroups.

Stronger properties

 * Weaker than::Subgroup realizable as the commutator of the whole group and a subgroup
 * Member of the lower central series
 * Member of the derived series
 * Weaker than::Perfect normal subgroup

Weaker properties

 * Stronger than::Subgroup realizable as the commutator of two subsets