Section ExponentAbelem.
Variable gT : finGroupType.
Implicit Types (p n : nat) (pi : nat_pred) (x : gT) (A B C : {set gT}).
Implicit Types E G H K P X Y : {group gT}.
Arguments exponentP {A n}.

Lemma abelem_order_p p G x : p.-abelem G -> x \in G -> x != 1 -> #[x] = p.