Contents
Preface vi i
Prerequisites and Notation 1
Chapter 1: Introductio n
1.1. Geometric , Linear an d Projective Transformation s 2
1.2. Radiation s 4
1.3. Residue s 4
1.4. Transvection s 6
1.5. Matrice s 1
1.6. Projectiv e Transvection s 1
1.7. Comment s 1
Chapter 2: Generatio n Theorems
2.1. Generatio n b y Transvection s 1
2.2. Comment s 1
Chapter 3: Structur e Theory
3.1. Order s of Linea r Group s 2
3.2. Center s 2
3.3. Commutato r Subgroup s 2
3.4. Simplicit y Theorem s 2
3.5. Anothe r Approac h t o Simplicit y 2
3.6. Comment s 2
Chapter 4: CoUinea r Transformations and Projective Geometry
4.1. Semilinea r Algebr a 2
4.2. Th e Fundamenta l Theore m o f Projective Geometr y 3
4.3. Th e Groups TL n{V) an d FTLJV) 3
4.4. Th e Isomorphism s &
g
3
4.5. Th e Contragredient 3
4.6. Comment s 3
Chapter 5: Th e Isomorphisms of Linea r Groups
5.1. Preliminarie s 4
5.2. Ful l groups 4
5.3. CDC i n th e Linea r Cas e 4
5.4. Preservatio n o f Projective Transvection s i n th e Linea r Cas e 5
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