1547845830-Classification_of_Quasithin_Groups_-_Volume_II__Aschbacher_

1166 15. THE CASE .Cr(G, T) = 0

Although by this point it may feel like something of an anticlimax, we have also

completed the proof of the Main Theorem: For suppose G is a simple QTKE-group,

with TE Syb(G). If JM(T)J = 1, the groups appearing as conclusions in Theorem

2.1.1 of chapter 2 appear as conclusions in the Main Theorem. So assume that

JM(T)J > 1. If CJ(G,T) = 0, then the groups in the conclusion of Theorem E are

among those in the conclusion of the Main Theorem. Finally if CJ(G, T) of. 0, then

the groups in the conclusion of Theorem D (14K2) appear as conclusions in the

Main Theorem.

Thus, after a hiatus of roughly twenty years, there is at last a classification of

the quasi thin groups of even characteristic. In particular, this result fills that gap

in the literature classifying the finite simple groups.