(* Note: 'nosimpl' MUST be used outside of a section -- the end of section    *)
(* "cooking" destroys it.                                                     *)
Definition upper_central_at := nosimpl upper_central_at_rec.Notation "''Z_' n ( G )" := (upper_central_at n G)
  (at level 8, n at level 2, format "''Z_' n ( G )") : group_scope.'N('Z_n(G)). Proof. exact: gFnorm. Qed.
Lemma ucn_normal : 'Z_n(G) <| G. Proof. exact: gFnoCanonical lower_central_at_group n G := Group (lcn_group_set n G).

(* Specifications: *)
Lemma lcnP G : reflect (exists n, 'L_n.+1(G) =