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

(* Part of Aschbacher (18.7.4). *)
Lemma coprime_norm_cent A G :
A \subset 'N(G) -> coprime #|G| #|A| -> 'N_G(A) = 'C_G(A).