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 comm3G1P A B C :
reflect {in A & B & C, forall h k l, [~ h, k, l] = 1} ([~: A, B, C] :==: 1).