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
Description:
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.
Download or read it online for free here:
Download link
(1.8MB, PDF)
Similar books
Lectures On Galois Cohomology of Classical Groupsby M. Kneser - Tata Institute of Fundamental Research
The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.
(6923 views)
Lectures on Field Theory and Ramification Theoryby Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.
(7239 views)
Galois Theoryby Miles Reid - University of Warwick
The author discusses the problem of solutions of polynomial equations both in explicit terms and in terms of abstract algebraic structures. The course demonstrates the tools of abstract algebra as applied to a meaningful problem.
(12432 views)
The Elements of the Theory of Algebraic Numbersby Legh Wilber Reid - The Macmillan company
It has been my endeavor in this book to lead by easy stages a reader, entirely unacquainted with the subject, to an appreciation of some of the fundamental conceptions in the general theory of algebraic numbers. Many numerical examples are given.
(6970 views)