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 coprime_p'group p K R :
coprime #|K| #|R| -> p.-group R -> R :!=: 1 -> p^'.-group K.