Section PgroupProps.
Variable gT : finGroupType.
Implicit Types (pi rho : nat_pred) (p : nat).
Implicit Types (x y z : gT) (A B C D : {set gT}) (G H K P Q R : {group gT}).

Lemma comm_sub_max_pgroup pi H M G :
[max M | pi.-subgroup(G) M] -> pi.-group H -> H \subset G ->
commute H M -> H \subset M.