Section SCNseries.
Variables A : {group gT}.
Hypothesis SCN_A : A \in 'SCN(G).
Let Z := 'Ohm_1(A).
Let cAA := SCN_abelian SCN_A.
Let sZA: Z \subset A := Ohm_sub 1 A.
Let nZA : A \subset 'N(Z) := sub_abelian_norm cAA sZA.
End SCNseries.

(* 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.