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 orderXprime p n x :
#[x ^+ p] = n -> prime p -> p %| n -> #[x] = (p * n)%N.