End StructureCorollaries.
End Extraspecial.
Section SCN.
Variables (gT : finGroupType) (p : nat) (G : {group gT}).
Implicit Types A Z H : {group gT}.

(* Specifications: *)
Lemma SCN_P A : reflect (A <| G /\ 'C_G(A) = A) (A \in 'SCN(G)).
(* SCN_max and max_SCN cover Aschbacher 23.15(1) *)
Lemma SCN_max A : A \in 'SCN(G) -> [max A | A <| G & abelian A].
Lemma max_SCN A :
p.-group G -> [max A | A <| G & abelian A] -> A \in 'SCN(G).