Contents Chapter 1. Introduction 1 Acknowledgment 2 Chapter 2. Definition 3 Chapter 3. Some Identities 7 Chapter 4. From Quadrangular Systems To Moufang Quadrangles 15 Chapter 5. From Moufang Quadrangles To Quadrangular Systems 23 Chapter 6. Some Remarks 35 Chapter 7. Examples 37 7.1. Quadrangular Systems of Quadratic Form Type 37 7.2. Quadrangular Systems of Involutory Type 37 7.3. Quadrangular Systems of Indifferent Type 38 7.4. Quadrangular Systems of Pseudo-quadratic Form Type 39 7.5. Quadrangular Systems of Type EQ, Ej and Eg 40 7.6. Quadrangular Systems of Type F4 43 Chapter 8. The Classification 47 8.1. Quadrangular Systems of Involutory Type 49 8.2. Quadrangular Systems of Quadratic Form Type 60 8.3. Quadrangular Systems of Indifferent Type 63 8.4. Quadrangular Systems of Pseudo-quadratic Form Type, I 65 8.5. Quadrangular Systems of Type F4 70 8.6. Quadrangular Systems of Pseudo-quadratic Form Type, II 81 8.7. Quadrangular Systems of Type EQ, Ej and E$ 93 Appendix A. Abelian Quadrangular Systems 95 A.l. Reduced Quadrangular Systems 96 A.2. Indifferent Quadrangular Systems 96 A.3. Radical Quadrangular Systems 97 Appendix. Bibliography 99
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