Definition Zgroup (gT : finGroupType) (A : {set gT}) :=
[forall (V : {group gT} | Sylow A V), cyclic V].
Section Zgroups.
Variables (gT rT : finGroupType) (D : {group gT}) (f : {morphism D >-> rT}).
Implicit Types G H K : {group gT}.

(* Specifications: *)
Lemma ZgroupS G H : H \subset G -> Zgroup G -> Zgroup H.
Lemma morphim_Zgroup G : Zgroup G -> Zgroup (f @* G).
Lemma nil_Zgroup_cyclic G : Zgroup G -> nilpotent G -> cyclic G.
End Zgroups.