**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

**Fields and Galois Theory**

by

**J. S. Milne**

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.

(

**7635**views)

**The Elements of the Theory of Algebraic Numbers**

by

**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.

(

**5694**views)

**Galois Theory: Lectures Delivered at the University of Notre Dame**

by

**Emil Artin**-

**University of Notre Dame**

The book deals with linear algebra, including fields, vector spaces, homogeneous linear equations, and determinants, extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, and more.

(

**1888**views)

**Class Field Theory**

by

**J. S. Milne**

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.

(

**7045**views)