Canonical lcn_gFun n := [gFun by lcn_cont n].
Canonical lcn_mgFun n := [mgFun by fun _ G H => @lcnS _ n G H].
Section UpperCentralFunctor.
Variable n : nat.
Implicit Type gT : finGroupType.

Lemma ucnSnR n G : 'Z_n.+1(G) = [set x in G | [~: [set x], G] \subset 'Z_n(G)].