Stable Groups

by F. Wagner

Overview

The study of stable groups connects model theory, algebraic geometry and group theory. It analyzes groups that possess a certain general dependence relation 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 current knowledge in the field.

Product Details

ISBN-13:	9780521598392
Publisher:	Cambridge University Press
Publication date:	08/21/1997
Series:	London Mathematical Society Lecture Note Series , #240
Pages:	320
Product dimensions:	5.98(w) x 9.02(h) x 0.71(d)

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.

Editorial Reviews

' … 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

From the Publisher