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Generic polynomials : constructive aspects of the inverse Galois problem

By: Contributor(s): Material type: TextTextLanguage: English Series: Mathematical sciences research institute publications ; 45Publication details: Cambridge; Cambridge University Press; 2002Description: ix, 258p. illISBN:
  • 9780521819985 (HB)
Subject(s):
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
Summary: 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.
Item type: BOOKS
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Home library Call number Materials specified Status Date due Barcode
IMSc Library 511.331 JEN (Browse shelf(Opens below)) Available 60431

Includes index

Includes bibliography (p. 247-253) and references

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

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.

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The Institute of Mathematical Sciences, Chennai, India