**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.

(

**7218**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.

(

**5248**views)

**Lectures on Field Theory and Ramification Theory**

by

**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.

(

**5709**views)

**Lectures on the Algebraic Theory of Fields**

by

**K.G. Ramanathan**-

**Tata Institute of Fundamental Research**

These lecture notes on Field theory are aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. We assume a familiarity with group theory and vector spaces.

(

**6484**views)