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 sub_der1_norm G H : G^`(1) \subset H -> H \subset G -> G \subset 'N(H).