Section Cyclic.
Variable gT : finGroupType.
Implicit Types (a x y : gT) (A B : {set gT}) (G K H : {group gT}).
Definition cyclic A := [exists x, A == <[x]>].
Canonical Zpm_morphism := Morphism ZpmM.

Lemma cyclic_dprod K H G :
K \x H = G -> cyclic K -> cyclic H -> cyclic G = coprime #|K| #|H| .