End ExtremalClass.

(* This is the second part of Aschbacher, exercise (8.4). *)
Lemma prime_Ohm1P gT p (G : {group gT}) :
p.-group G -> G :!=: 1 ->
reflect (#|'Ohm_1(G)| = p)
(cyclic G || (p == 2) && (extremal_class G == Quaternion)).