Stable Groups

F. Wagner

• Publisher: Cambridge University Press
• Year: 1997
• ISBN:
  9781107108943
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Series Page
• Title
• Copyright
• Dedication
• Table of Contents
• Groups & Gist: Preface
• Groups & Gratitude: Acknowledgements
• Chapter 0 Groups & Goals
• Chapter 1 Groups & Generality
• Chapter 2 Groups & Genericity
• Chapter 3 Groups & Grandeur
• Chapter 4 Groups & Geometry
• Chapter 5 Groups & Grades
• Groups & Glory: References
• Groups & Gobbledegook: Index