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 ucn_cprod n A B G : A \* B = G -> 'Z_n(A) \* 'Z_n(B) = 'Z_n(G).