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

(* Another special case of the strong coprime quotient lemma; not found in    *)
(* textbooks, but nevertheless used implicitly throughout B & G, sometimes    *)
(* justified by switching to external action.                                 *)
Lemma quotient_TI_subcent K G H :
G \subset 'N(K) -> G \subset 'N(H) -> K :&: H = 1 ->
'C_K(G) / H = 'C_(K / H)(G / H).