Generic Polynomials: Constructive Aspects of the Inverse Galois Problem by C. U. Jensen, A. Ledet, N. Yui

Generic Polynomials: Constructive Aspects of the Inverse Galois Problem

Generic Polynomials: Constructive Aspects of the Inverse Galois Problem by C. U. Jensen, A. Ledet, N. Yui
Publisher: Cambridge University Press 2002
ISBN/ASIN: 0521819989
ISBN-13: 9780521819985
Number of pages: 268
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.
Mathematics Abstract Algebra Fields & Galois Theory

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Generic Polynomials: Constructive Aspects of the Inverse Galois Problem by C. U. Jensen, A. Ledet, N. Yui