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 orderM a b :
commute a b -> coprime #[a] #[b] -> #[a * b] = (#[a] * #[b])%N.