Groups & Gist: Preface -- Groups & Gratitude: Acknowledgements -- 0. Groups & Goals -- 1. Groups & Generality -- 2. Groups & Genericity -- 3. Groups & Grandeur -- 4. Groups & Geometry -- 5. Groups & Grades -- Groups & Glory: References -- Groups & Gobbledegook: Index.
Summary
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.
