Stable Groups
The study of stable groups connects model theory, algebraic geometry and group theory. It analyses groups which possess a certain very general dependence relation (Shelah's notion of 'forking'), and tries to derive structural properties from this. These may be group-theoretic (nilpotency or solubility of a given group), algebro-geometric (identification of a group as an algebraic group), or model-theoretic (description of the definable sets). In this book, the general theory of stable groups is developed from the beginning (including a chapter on preliminaries in group theory and model theory), concentrating on the model- and group-theoretic aspects. It brings together the various extensions of the original finite rank theory under a unified perspective and provides a coherent exposition of the knowledge in the field.
- Self-contained treatment
- Up-to-date research
- Topical subject matter
Reviews & endorsements
' … a valuable addition to the model-theoretic literature'. Dugald MacPherson, Bulletin of the London Mathematical Society
'This book presents the state-of-the-art of the field …' Zentralblatt für Mathematik und ihre Grenzgebiete
'… an original contribution to the theory.' A. Baudisch, Niew Archief voor Wiskunde
Product details
August 1997Paperback
9780521598392
320 pages
229 × 152 × 18 mm
0.47kg
Available
Table of Contents
- 1. Groups and goals
- 2. Groups and generality
- 3. Groups and genericity
- 4. Groups and grandeur
- 5. Groups and geometry
- 6. Groups and grades
- Bibliography.
