End SomeHall.
Section Nilpotent.
Variable gT : finGroupType.
Implicit Types (G H K P L : {group gT}) (p q : nat).

Lemma sub_nilpotent_cent2 H K G :
nilpotent G -> K \subset G -> H \subset G -> coprime #|K| #|H| ->
H \subset 'C(K).