Section GeneralExponentPextraspecialTheory.
Variable p : nat.

(* This is Aschbacher (23.12) *)
Lemma Ohm1_extraspecial_odd (gT : finGroupType) (G : {group gT}) :
p.-group G -> extraspecial G -> odd #|G| ->
let Y := 'Ohm_1(G) in
[/\ exponent Y = p, #|G : Y| %| p
& Y != G ->
exists E : {group gT},
[/\ #|G : Y| = p, #|E| = p \/ extraspecial E,
exists2 X : {group gT}, #|X| = p & X \x E = Y
& exists M : {group gT},
[/\ M \isog 'Mod_(p ^ 3), M \* E = G & M :&: E = 'Z(M)]]].