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Generic Polynomials

Generic Polynomials
Constructive Aspects of the Inverse Galois Problem

Out of Print

Part of Mathematical Sciences Research Institute Publications

  • Date Published: February 2003
  • availability: Unavailable - out of print
  • format: Hardback
  • isbn: 9780521819985

Out of Print
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  • This book describes a constructive approach to the Inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G. Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G. The main theme of the book is an exposition of a family of 'generic' polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group. The existence of such generic polynomials is discussed, and where they do exist, a detailed treatment of their construction is given. The book also introduces the notion of 'generic dimension' to address the problem of the smallest number of parameters required by a generic polynomial.

    • The first monograph addressing 'generic polynomials' systematically
    • A new concept of 'generic dimensions' is introduced
    • Numerous explicit examples of generic polynomials
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    Product details

    • Date Published: February 2003
    • format: Hardback
    • isbn: 9780521819985
    • length: 268 pages
    • dimensions: 244 x 160 x 20 mm
    • weight: 0.509kg
    • contains: 7 b/w illus. 1 table 88 exercises
    • availability: Unavailable - out of print
  • Table of Contents

    Introduction
    1. Preliminaries
    2. Groups of small degree
    3. Hilbertian fields
    4. Galois theory of commutative rings
    5. Generic extensions and generic polynomials
    6. Solvable groups I: p-groups
    7. Solvable groups II: Frobenius groups
    8. The number of parameters
    Appendix A. Technical results
    Appendix B. Invariant theory
    Bibliography
    Index.

  • Authors

    Christian U. Jensen, University of Copenhagen

    Arne Ledet, Texas Tech University

    Noriko Yui, Queen's University, Ontario

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