End ModularGroupAction.
Section Sylow.
Variables (p : nat) (gT : finGroupType) (G : {group gT}).
Implicit Types P Q H K : {group gT}.

Lemma Sylow_subJ P Q :
p.-Sylow(G) P -> Q \subset G -> p.-group Q ->
exists2 x, x \in G & Q \subset P :^ x.