End GeneralExponentPextraspecialTheory.

(* The uniqueness half of Achsbacher (23.14). The proof incorporates in part  *)
(* the proof that symplectic spces are hyperbolic (Aschbacher (19.16)), and   *)
(* the determination of quadratic spaces over 'F_2 (21.2); however we use     *)
(* the second part of exercise (8.4) to avoid resorting to Witt's lemma and   *)
(* Galois theory as in (20.9) and (21.1).                                     *)
Lemma isog_2extraspecial (gT : finGroupType) (G : {group gT}) n :
#|G| = (2 ^ n.*2.+1)%N -> extraspecial G -> G \isog 'D^n \/ G \isog 'D^n.-1*Q.