Stable groups

Frank O. Wagner

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.

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[目次]

  • 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.

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この本の情報

書名 Stable groups
著作者等 Wagner, Frank O.
Wagner F.
シリーズ名 London Mathematical Society lecture note series
出版元 Cambridge University Press
刊行年月 1997
ページ数 ix, 309 p.
大きさ 23 cm
ISBN 0521598397
NCID BA31887648
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言語 英語
出版国 イギリス
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