Canonical derived_at_group G n := Group (der_group_set G n).Notation "G ^` ( n )" := (derived_at_group G n) : Group_scope.Implicit Types x y z : gT.Implicit Type (rT : finGroupType) (A B C : {set gT}) (D G H K : {group gT}).

Lemma derG1P G : reflect (G^`(1) = 1) (abelian G).