Generic Polynomials
Generic Polynomials
Arne Ledet, Texas Tech University
Noriko Yui, Queen's University, Ontario
Mathematical Sciences Research Institute
Out of Print
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
Reviews & endorsements
"...a clearly written book, which uses (almost) exclusively algebraic language (and no cohomology), and which will be useful for every algebraist or number theorist. It is easily accessible and suitable also for first-year graduate students." Mathematical Reviews
Product details
December 2002Hardback
9780521819985
268 pages
244 × 160 × 20 mm
0.509kg
7 b/w illus. 1 table 88 exercises
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.
