End HallCorollaries.
Section InternalAction.
Variables (pi : nat_pred) (gT : finGroupType).
Implicit Types G H K A X : {group gT}.

(* A complement to the above: 'C(A) acts on 'Nby(A) *)
Lemma norm_conj_cent A G x : x \in 'C(A) ->
(A \subset 'N(G :^ x)) = (A \subset 'N(G)).