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 0 1.6. Projectiv e Transvection s 1 1 1.7. Comment s 1 2 Chapter 2: Generatio n Theorems 2.1. Generatio n b y Transvection s 1 4 2.2. Comment s 1 9 Chapter 3: Structur e Theory 3.1. Order s of Linea r Group s 2 0 3.2. Center s 2 1 3.3. Commutato r Subgroup s 2 1 3.4. Simplicit y Theorem s 2 3 3.5. Anothe r Approac h t o Simplicit y 2 5 3.6. Comment s 2 7 Chapter 4: CoUinea r Transformations and Projective Geometry 4.1. Semilinea r Algebr a 2 8 4.2. Th e Fundamenta l Theore m o f Projective Geometr y 3 0 4.3. Th e Groups TL n {V) an d FTLJV) 3 3 4.4. Th e Isomorphism s & g 3 5 4.5. Th e Contragredient 3 6 4.6. Comment s 3 8 Chapter 5: Th e Isomorphisms of Linea r Groups 5.1. Preliminarie s 4 0 5.2. Ful l groups 4 2 5.3. CDC i n th e Linea r Cas e 4 5 5.4. Preservatio n o f Projective Transvection s i n th e Linea r Cas e 5 1 v
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