Groups of Finite Morley Rank [Hardcover]

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.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-GroupsAppendix A: Miscellaneous ResultsAppendix B: Open ProblemsAppendix C: Link with Model TheoryAppendix D: Hints to the Exercises 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 [and] 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 to anyone, researcher or graduate student, interested in the connection of model theory and group theory. --Journal of Symbolic Logic