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Generic Polynomials: Constructive Aspects of the Inverse Galois Problem
     

Generic Polynomials: Constructive Aspects of the Inverse Galois Problem

by Christian U. Jensen, Arne Ledet, Noriko Yui
 

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ISBN-10: 0521819989

ISBN-13: 9780521819985

Pub. Date: 03/01/2003

Publisher: Cambridge University Press

This book describes a constructive approach to the Inverse Galois problem. The main theme 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

Overview

This book describes a constructive approach to the Inverse Galois problem. The main theme 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.

Product Details

ISBN-13:
9780521819985
Publisher:
Cambridge University Press
Publication date:
03/01/2003
Series:
Mathematical Sciences Research Institute Publications Series , #45
Edition description:
New Edition
Pages:
268
Product dimensions:
6.14(w) x 9.21(h) x 0.79(d)

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.

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