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 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
Appendix A: Miscellaneous Results
Appendix B: Open Problems
Appendix C: Link with Model Theory
Appendix 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