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

(* A useful consequence (similar to Ex. 6.1 in Aschbacher) of the stronger   *)
(* theorem. *)
Lemma coprime_cent_mulG A G H :
A \subset 'N(G) -> A \subset 'N(H) -> G \subset 'N(H) ->
coprime #|H| #|A| -> solvable H ->
'C_(H * G)(A) = 'C_H(A) * 'C_G(A).