1547845830-Classification_of_Quasithin_Groups_-_Volume_II__Aschbacher_

(jair2018) #1

xii


14.1.
14.2.
14.3.
14.4.
14.5.
14.6.
14.7.
14.8.

CONTENTS

Preliminary results for the case .Cr(G, T) empty

Starting the L 2 (2) case of .Cr empty
First steps; reducing (VG^1 ) nonabelian to extraspecial
Finishing the treatment of (VG^1 ) nonabelian
Starting the case (VG^1 ) abelian for L 3 (2) and L 2 (2)
Eliminating L 2 (2) when (VG^1 ) is abelian
Finishing L 3 (2) with (VG^1 ) abelian
The QTKE-groups with .Cr(G, T) f:. 0

975

981

989

1005

1013

1020

1042

1078

Part 6. The case .C1(G, T) empty^1081


1083
1083
1104
1120
1155

Chapter 15. The case .Cr(G, T) = 0


15.1.' Initial reductions when .Cr(G, T) is empty

15.2. Finishing the reduction to Mr/CMr(V(Mr)) c:=. OJ(2)

15.3. The elimination of Mr/CMr(V(Mr)) = Ss wr Z

15.4. Completing the proof of the Main Theorem

Part 7. The Even Type Theorem 1167


Chapter 16. Quasithin groups of even type but not even characteristic 1169

16.1. Even type groups, and components in centralizers 1169
16.2. Normality and other properties of components 1173
16.3. Showing L is standard in G 1177
16.4. Intersections of NG(L) with conjugates of CG(L) 1182
16.5. Identifying J 1, and obtaining the final contradiction 1194

Bibliography and Index 1205


Background References Quoted
(Part 1: also used by GLS) 1207

Background References Quoted

(Part 2: used by us but not by GLS) 1209

Expository References Mentioned 1211


Index 1215

Free download pdf