Groups of Finite Morley Rank

Hardcover | April 30, 1999

byAlexandre Borovik, Ali Nesin

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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 thesubject 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 inlength. 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.

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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 thesubject and to prepare the graduate student...

Alexandre Borovik is at University of Manchester Institute of Science and Technology. Ali Nesin is at University of California at Irvine.

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Format:HardcoverDimensions:426 pages, 9.21 × 6.14 × 1.1 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534450

ISBN - 13:9780198534457

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Table of Contents

1. Basic Group Theory2. Definability3. Interpretability4. Ranked Universe5. Basic Properties6. Nilpotent Groups7. Semisimple Groups8. Fields and Rings9. Solvable Groups10. 2-Sylow Theory11. Permutation Groups12. Gepometrics13. bad Groups14. CN and CIT-GroupsA. Miscellaneous ResultsB. Open ProblemsC. Link with Model TheoryD. Hints to the ExercisesBibliographyIndex

Editorial Reviews

"The book is excellently written, and great care has been taken to make it accessible to group theorists. It is liberally laced with exercises, particularly in the beginning, and it is made clear when these are important to the theory." -- Mathematical Reviews"Fascinating. . .Gives an impressive amount of very beautiful mathematics, and in a very elegant way Ýand¨ shows a multitude of ways to attack the problem. . . .The book also contains an important list of open problems and a very complete bibliography. . . .I will strongly recommend this book toanyone, researcher or graduate student, interested in the connection of model theory and group theory."--Journal of Symbolic Logic