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 pgroup_pdiv p G :
p.-group G -> G :!=: 1 ->
[/\ prime p, p %| #|G| & exists m, #|G| = p ^ m.+1]%N.