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.Read more
- 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 SocietySee more reviews
'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
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- Date Published: August 1997
- format: Paperback
- isbn: 9780521598392
- length: 320 pages
- dimensions: 229 x 152 x 18 mm
- weight: 0.47kg
- availability: 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
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