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 pmaxElemP p A E :
reflect (E \in 'E_p(A) /\ forall H, H \in 'E_p(A) -> E \subset H -> H :=: E)
(E \in 'E*_p(A)).