Model Theory of Groups and Automorphism Groups
Model Theory of Groups and Automorphism Groups
AUD$98.95
inc GSTThis volume surveys recent interactions between model theory and other branches of mathematics, notably group theory. Beginning with an introductory chapter describing relevant background material, the book contains contributions from many leading international figures in this area. Topics described include automorphism groups of algebraically closed fields, the model theory of pseudo-finite fields and applications to the subgroup structure of finite Chevalley groups. Model theory of modules, and aspects of model theory of various classes of groups, including free groups, are also discussed. The book also contains the first comprehensive survey of finite covers. Many new proofs and simplifications of recent results are presented and the articles contain many open problems. This book will be a suitable guide for graduate students and a useful reference for researchers working in model theory and algebra.
- Contains introductory material, articles include many open problems
- Contributors are leading international figures in the field
- In highly respected series
Reviews & endorsements
'The interesting articles range from purely group theoretic ones to mainly model theoretic ones … and reflect impressively the prolific interaction between these two fields.' Monatshefte für Mathematik
Product details
September 1997Paperback
9780521589550
232 pages
229 × 153 × 15 mm
0.315kg
7 b/w illus. 14 music examples 14 exercises
Available
Table of Contents
- Preface
- 1. Introduction
- 2. Finite covers
- 3. Definable subgroups of algebraic groups over pseudo-finite fields
- 4. Groups in pseudo-finite fields
- 5. The groups of automorphisms of the field of complex numbers leaving fixed the algebraic numbers are simple
- 6. The automorphism groups of the field of complex numbers are complete
- 7. The algebra of an age
- 8. Elimination of inverses in groups
- 9. Model-theoretic properties of polycyclic-by-finite groups
- 10. Non-standard free groups
- 11. Finitely generated subgroups of the free Z(t)-group on two generators
- 12. Rings of definable scalars and biendomorphism rings
- 13. Recent results on simple first-order theories.
