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Klappentext This book clearly details the theory of groups of finite Morley rank--groups which arise in model theory and generalize the concept of algebraic groups over algebraically closed fields. Written especially for pure group theorists and graduate students embarking on research on the subject, the book develops the theory from the beginning and contains an algebraic and self-evident rather than a model-theoretic point of view. All necessary model and group theoretical notions are explained at length. Containing nearly all of the known results in the subject, the book offers a plethora of exercises and examples, making it ideal for both students and researchers in group theory and model theory. Zusammenfassung The book is devoted to the theory of groups of finite Morley rank. These groups arise in model theory and generalize the concept of algebraic groups over algebraically closed fields. The book contains almost all the known results in the subject. Trying to attract pure group theorists in the subject and to prepare the graduate student to start the research in the area, the authors adopted an algebraic and self evident point of view rather than a model theoretic one, and developed the theory from scratch. All the necessary model theoretical and group theoretical notions are explained in length. The book is full of exercises and examples and one of its chapters contains a discussion of open problems and a program for further research. Inhaltsverzeichnis 1: Basic Group Theory 2: Definability 3: Interpretability 4: Ranked Universe 5: Basic Properties 6: Nilpotent Groups 7: Semisimple Groups 8: Fields and Rings 9: Solvable Groups 10: 2-Sylow Theory 11: Permutation Groups 12: Gepometrics 13: bad Groups 14: CN and CIT-Groups A. Miscellaneous Results B. Open Problems C. Link with Model Theory D. Hints to the Exercises Bibliography Index
