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  1. Home
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  3. Stable Groups
  • Cited by 27
Publisher:
Cambridge University Press
Online publication date:
April 2013
Print publication year:
1997
Online ISBN:
9780511566080
DOI:
https://doi.org/10.1017/CBO9780511566080
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
Series:
London Mathematical Society Lecture Note Series (240)
Information

Book description

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.

Reviews

‘ … a valuable addition to the model-theoretic literature’.

Dugald MacPherson Source: Bulletin of the London Mathematical Society

‘This book presents the state-of-the-art of the field …’

Source: Zentralblatt für Mathematik und ihre Grenzgebiete

‘… an original contribution to the theory.’

A. Baudisch Source: Niew Archief voor Wiskunde

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