Introduction Chapter 1.Affine and Projective Planes 1.1.Preview 1.2.Incidence geometry 1.3.Affine planes 1.4.Projective planes 1.5.Duality 1.6.Exercises Chapter 2.Central Automorphisms of Projective Planes 2.1.Preview 2.2.Projections and automorphisms 2.3.Transvections and dilatations 2.4.Transitivity properties 2.5.Exercises Chapter 3.Coordinates for Projective Planes 3.1. Preview 3.2.Ternary systems 3.3.Two coordinatizations related to G(C) 3.4.Transvections and algebraic properties 3.5.Exercises Chapter 4.Alternative Rings 4.1.Preview 4.2.Left Moufang rings 4.3.Artin's Theorem 4.4.Inverses in alternative rings 4.5. The Cayley-Dickson process 4.6.Composition algebras 4.7.Split and division composition algebras 4.8.Exercises Chapter 5.Configuration Conditions 5.1.Preview 5.2.Desargues condition 5.3.Quadrangle sections 5.4.Pappus condition 5.5.Configurations and central automorphisms 5.6.Exercises Chapter 6.Dimension Theory 6.1.Preview 6.2.Dimensionable sets 6.3.Independence and bases 6.4.Strongly dimensionable sets 6.5.Exercises Chapter 7.Projective Geometries 7.1.Preview 7.2.Projective and nearly projective geometries 7.3.Relation to strongly dimensionable sets 7.4.Classification of projective geometries 7.5.Exercises Chapter 8. Automorphisms of g(V) 8.1.Preview
8.2.The Fundamental Theorem 8.3.Subgroups of Aut(C(V)) 8.4.Simple groups 8.5.Exercises Chapter 9.Quadratic Forms and Orthogonal Groups 9.1.Preview 9.2.Quadratic formsidapin oldumonus buo shue 9.3.Orthogonal groups 9.4.Exercises Chapter 10.Homogeneous Maps 10.1. Preview 10.2.Polarization of homogeneous maps 10.3.Exercises Chapter 11.Norms and Hermitian Matrices 11.1.Preview 11.2.Hermitian matrices and HE,(C) 11.3.Norms on H(Cn) 11.4.Transitivity of HE,(C) 11.5.Trace and adjoint 11.6.H(C3) 11.7.Exercises Chapter 12.Octonion Planes 12.1.Preview 12.2.The construction of octonion planes 12.3.Simplicity of PHE3(O) 12.4.Automorphisms of octonion planes 12.5.Exercises Chapter 13.Projective Remoteness Planes 13.1.Preview 13.2.Definition and examples 13.3.Groups of Steinberg type 13.4.Transvections 13.5.Exercises Chapter 14.Other Geometries 14.1.Preview 14.2.Erlangen program 14.3.The geometry of R-spaces 14.4.Buildings 14.5.Generalized n-gons 14.6.Moufang sets and structurable algebras 14.7.Freudenthal-Tits magic square 14.8.Exercises Bibliography Index
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