Arguments Ohm n%N {gT} A%g.
Arguments Ohm_group n%N {gT} A%g.
Arguments Mho n%N {gT} A%g.
Arguments Mho_group n%N {gT} A%g.
Arguments OhmPredP {n gT x}.
Notation "''Ohm_' n ( G )" := (Ohm n G)
(at level 8, n at level 2, format "''Ohm_' n ( G )") : group_scope.
Notation "''Ohm_' n ( G )" := (Ohm_group n G) : Group_scope.
Notation "''Mho^' n ( G )" := (Mho n G)
(at level 8, n at level 2, format "''Mho^' n ( G )") : group_scope.
Notation "''Mho^' n ( G )" := (Mho_group n G) : Group_scope.
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}.

Lemma exponentP A n :
reflect (forall x, x \in A -> x ^+ n = 1) (exponent A %| n).