Arguments Zgroup {gT} A%g.
Section NilPGroups.
Variables (p : nat) (gT : finGroupType).
Implicit Type G P N : {group gT}.

(* Specifications: *)
(* B & G 1.22 p.9 *)
Lemma normal_pgroup r P N :
p.-group P -> N <| P -> r <= logn p #|N| ->
exists Q : {group gT}, [/\ Q \subset N, Q <| P & #|Q| = (p ^ r)%N].
Theorem Baer_Suzuki x G :
x \in G -> (forall y, y \in G -> p.-group <<[set x; x ^ y]>>) ->
x \in 'O_p(G).