Generic Polynomials
Generic Polynomials
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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.
- 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
- Published: December 2002
- Format: Hardback
- ISBN: 9780521819985
- Length: 268 pages
- Dimensions: 244 × 160 × 20 mm
- Weight: 0.509kg
- Contains: 7 b/w illus. 1 table 88 exercises
- Availability: 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.
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