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}.
Arguments nElemP {n G E}.

Lemma nElem1P G E :
reflect (E \subset G /\ exists2 p, prime p & #|E| = p) (E \in 'E^1(G)).