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 cyclic_abelem_prime p X : p.-abelem X -> cyclic X -> X :!=: 1 -> #|X| = p.