End SCNseries.

(* Specifications: *)
(* This is Aschbacher 23.16. *)
Lemma Ohm1_cent_max_normal_abelem Z :
odd p -> p.-group G -> [max Z | Z <| G & p.-abelem Z] -> 'Ohm_1('C_G(Z)) = Z.
Lemma critical_class2 H : critical H G -> nil_class H <= 2.
(* This proof of the Thompson critical lemma is adapted from Aschbacher 23.6 *)
Lemma Thompson_critical : p.-group G -> {K : {group gT} | critical K G}.
Lemma critical_p_stab_Aut H :
critical H G -> p.-group G -> p.-group 'C(H | [Aut G]).