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Stable Groups
 
Bruno Poizat Université Claude Bernard, Villeurbanne, France
Stable Groups
eBook ISBN:  978-1-4704-1314-9
Product Code:  SURV/87.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Stable Groups
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Stable Groups
Bruno Poizat Université Claude Bernard, Villeurbanne, France
eBook ISBN:  978-1-4704-1314-9
Product Code:  SURV/87.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 872001; 129 pp
    MSC: Primary 03; 14; 20;

    This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects.

    The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described.

    The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.

    Readership

    Graduate students and research mathematicians working in logic and in algebra.

  • Table of Contents
     
     
    • Chapters
    • 1. Chain. The chain condition for stable groups
    • 2. Structure. Model-theoretic analysis of groups of finite Morley rank
    • 3. Fields. Algebraic properties of groups of finite Morley rank
    • 4. Geometry. Introduction to algebraic groups
    • 5. Generics. The reconstruction of a stable group from its generic fragments
    • 6. Rank. Superstable groups
    • 7. Weight. The last trick for shining in the salons
  • Reviews
     
     
    • From a review of the French edition:

      This is a beautiful book in which almost everything known about stable groups appears.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 872001; 129 pp
MSC: Primary 03; 14; 20;

This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects.

The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described.

The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.

Readership

Graduate students and research mathematicians working in logic and in algebra.

  • Chapters
  • 1. Chain. The chain condition for stable groups
  • 2. Structure. Model-theoretic analysis of groups of finite Morley rank
  • 3. Fields. Algebraic properties of groups of finite Morley rank
  • 4. Geometry. Introduction to algebraic groups
  • 5. Generics. The reconstruction of a stable group from its generic fragments
  • 6. Rank. Superstable groups
  • 7. Weight. The last trick for shining in the salons
  • From a review of the French edition:

    This is a beautiful book in which almost everything known about stable groups appears.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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