(* Lemmas bundling Aschbacher (23.10) with (19.1), (19.2), (19.12) and (20.8) *)
Section ExtraspecialFormspace.
Variable G : {group gT}.
Hypotheses (pG : p.-group G) (esG : extraspecial G).
Let p_pr := extraspecial_prime pG esG.
Let oZ := card_center_extraspecial pG esG.
Let p_gt1 := prime_gt1 p_pr.
Let p_gt0 := prime_gt0 p_pr.

(* This is the tranposition of the proof that the dimension of any maximal    *)
(* totally singular subspace is equal to the Witt index (Aschbacher (20.8)),  *)
(* to subgroups of an extraspecial group (in a slightly more general form,    *)
(* since we allow for p != 2).                                                *)
(*   Note that Aschbacher derives this from the Witt lemma, which we avoid.   *)
Lemma pmaxElem_extraspecial : 'E*_p(G) = 'E_p^('r_p(G))(G).
End ExtraspecialFormspace.