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  3. Stable Groups
  • Cited by 32
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 April 2013
      21 August 1997
      ISBN:
      9780511566080
      9780521598392
      DOI:
      https://doi.org/10.1017/CBO9780511566080
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.44kg, 320 Pages
      • Subjects:
      Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
      Series:
      London Mathematical Society Lecture Note Series (240)
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    • Selected: Digital
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    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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