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 abelemP p G :
prime p ->
reflect (abelian G /\ forall x, x \in G -> x ^+ p = 1) (p.-abelem G).