Logo

Generic Polynomials: Constructive Aspects of the Inverse Galois Problem

Large book cover: Generic Polynomials: Constructive Aspects of the Inverse Galois Problem

Generic Polynomials: Constructive Aspects of the Inverse Galois Problem
by

Publisher: Cambridge University Press
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.

Home page url

Download or read it online for free here:
Download link
(1.8MB, PDF)

Similar books

Book cover: Galois TheoryGalois Theory
by - 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.
(13901 views)
Book cover: Fields and Galois TheoryFields and Galois Theory
by
A concise treatment of Galois theory and the theory of fields, including transcendence degrees and infinite Galois extensions. Contents: Basic definitions and results; Splitting fields; The fundamental theorem of Galois theory; etc.
(10301 views)
Book cover: Geometry of the QuinticGeometry of the Quintic
by - Wiley-Interscience
The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem -- solving the quintic. This book helps students to develop connections between the algebra, geometry, and analysis ...
(8759 views)
Book cover: Class Field TheoryClass Field Theory
by
Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach.
(9634 views)