Generic polynomials : constructive aspects of the Inverse Galois problem
Author(s)
Bibliographic Information
Generic polynomials : constructive aspects of the Inverse Galois problem
(Mathematical Sciences Research Institute publications, 45)
Cambridge University Press, c2002
Available at 50 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. 247-253) and index
Description and Table of Contents
Description
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.
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.
by "Nielsen BookData"