Overview

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.

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9780511566080

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' ... 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 fur Mathematik und ihre Grenzgebiete '... an original contribution to the theory.' A. Baudisch, Niew Archief voor Wiskunde

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