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 cyclicM A B :
cyclic A -> cyclic B -> B \subset 'C(A) -> coprime #|A| #|B| ->
cyclic (A * B).