書誌事項

Generic polynomials : constructive aspects of the Inverse Galois problem

Christian U. Jensen, Arne Ledet, Noriko Yui

(Mathematical Sciences Research Institute publications, 45)

Cambridge University Press, c2002

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注記

Includes bibliographical references (p. 247-253) and index

内容説明・目次

内容説明

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.

目次

  • 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.

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詳細情報

  • NII書誌ID(NCID)
    BA60794198
  • ISBN
    • 0521819989
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    ix, 258 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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