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