End Basic_commutator_properties.
(***** Set theoretic commutators *****)
Section Commutator_properties.
Variable gT : finGroupType.
Implicit Type (rT : finGroupType) (A B C : {set gT}) (D G H K : {group gT}).

Lemma quotient_cents2r A B K :
[~: A, B] \subset K -> (A / K) \subset 'C(B / K).