Generic Polynomials: Constructive Aspects of the Inverse Galois Problem (Mathematical Sciences Research Institute Publications, Series Number 45) - Hardcover

Jensen, Christian U.; Ledet, Arne; Yui, Noriko

Hardcover

ISBN 10: 0521819989 ISBN 13: 9780521819985

Publisher: Cambridge University Press, 2002

Synopsis

This book describes a constructive approach to the Inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G. Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G. The main theme of the book 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.

About this title

Review

"...a clearly written book, which uses (almost) exclusively algebraic language (and no cohomology), and which will be useful for every algebraist or number theorist. It is easily accessible and suitable also for first-year graduate students." Mathematical Reviews

Book Description

The main theme in this book is a constructive approach to the Inverse Galois problem. The existence of certain 'Generic' polynomials, which give all Galois extensions having the required group as their Galois group, is demonstrated and where they do exist, a detailed treatment of their construction is given.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2002
• Language: English
• ISBN 10: 0521819989
• ISBN 13: 9780521819985
• Binding: Hardcover
• Number of pages: 268