Generic Polynomials

Constructive Aspects of the Inverse Galois Problem

Christian U. Jensen, Arne Ledet, Noriko Yui

268 pages, parution le 17/03/2003

Ajouter à une liste

Indisponible

Résumé

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.

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Christian U. Jensen, Arne Ledet, Noriko Yui
Parution	17/03/2003
Nb. de pages	268
Format	16 x 24
Couverture	Relié
Poids	510g
Intérieur	Noir et Blanc
EAN13	9780521819985
ISBN13	978-0-521-81998-5