List of Tables

Chapter 1

1.8. Irreducible reduced crystallographic root systems 12

1.12.5. Centers of universal Chevalley groups 19

1.12.6. Generators of Z(K) 20

1.15.2d. Graph automorphisms and their centralizers 28

Chapter 2

2.2. Orders of the finite groups of Lie type 39

2.3.2d. Twisted root systems 42

2.4. Structure of root groups X& 46

2.4.7. Elements of Cartan subgroups 51

2.5.12c. Structure of Outdiag(if) 58

Chapter 3

3.3.1. Equicharacteristic ranks of groups of Lie type 108

3.3.2. Cardinalities of abelian sets of roots 112

Chapter 4

4.3.1. Inn(if) -conjugacy classes of involutions in Auto (if),

an^

their cen-

tralizers 145

4.3.2. Centers of centralizers of involutions in Auto (if) 149

4.3.3. Connected centralizers of involutions in Auto (if) 151

4.3.4. Action of elements of V-^ on centralizers of involutions 152

4.5.1. Inner-diagonal and graph involutions for adjoint groups in Lieir),

r odd 172

4.5.2. Inner-diagonal and graph involutions for universal groups in £ie(r),

r odd 178

4.5.3. Inner-diagonal and graph involutions for ^|

m

(g) = D^q), q odd 182

4.5.5. Fundamental involutions 185

4.7.1. Inn(if)-conjugacy classes of subgroups of order p in exceptional

groups Auto (if), their centralizers and normalizers 206

4.7.2. Action of elements of T-^ on centralizers in exceptional groups if 208

4.7.3A. Conjugacy classes and centralizers of subgroups of order 3 for ex-

ceptional groups in Lie(r) 210

4.7.3B. Conjugacy classes and centralizers of subgroups of order 5 in E$(q) 211

4.10.6. Maximal commuting sets S(P) of fundamental subgroups, K G

ehev(r), r odd 244