Inverse Galois Theory / Edition 1

by Gunter Malle, B.H. Matzat

Overview

(Springer Monographs in Mathematics) Inverse Galois Theory is concerned with the question: which finite groups occur as Galois Groups over a given field? In particular, this includes the question on the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations. Contents: The Rigidity Method.- Applications of Rigidity.- Action of Braids.- Embedding Problems.- Rigid Analytic Methods.- Appendix: Example Polynomials.

Product Details

ISBN-13:	9783540628903
Publisher:	Springer Berlin Heidelberg
Publication date:	12/20/2002
Series:	Springer Monographs in Mathematics
Edition description:	1999
Pages:	437
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About the Author

Gunter Malle is professor of mathematics at the TU Kaiserslautern, Germany. He completed his doctorate at the TH Karlsruhe in 1986 with a dissertation on "Exzeptionelle Gruppen vom Lie-Typ als Galoisgruppen". He obtained his first professorship at Kassel University in 1998, and in 2005 was offered his current position. His research focus is on group representation theory and number theory. He is the coauthor of the books "Linear Algebraic Groups and Finite Groups of Lie Type" and "Inverse Galois Theory" as well as of multiple journal articles. He is currently serving on the editorial boards of six journals.

Bernd Heinrich Matzat is professor of mathematics at the University of Heidelberg, Germany. In 1972 he earned his doctorate at the University of Karlsruhe with a dissertation on "Über Weierstraßpunkte von Fermatkörpern", and in 1981 his Dr. habil. with the paper "Zur Konstruktion von Zahl- und Funktionenkörpern mit vorgegebenen Galoisgruppen". His first professorship was at the TU Berlin in 1987 and he moved from there to Heidelberg University in 1988. His research focus is on inverse Galois theory and differential Galois theory. He is author of the books "Konstruktive Galoistheorie", "Algorithmic algebra and number theory" and "Inverse Galois Theory" as well as of multiple journal articles.

Table of Contents

I.The Rigidity Method.- II. Applications of Rigidity.- III. Action of Braids.- IV. Embedding Problems.- V. Additive Polynomials.- VI.Rigid Analytic Methods.- Appendix: Example Polynomials.- References.- Index.

Editorial Reviews

The book presents the fundamental methods, models and techniques of grey data analysis, providing readers an overall picture and most recent research results of grey systems theory and its applications in a comprehensive and systematic fashion. … The book is written by distinguished experts in the field of grey systems theory and constitutes an up-to-date and complete guide on the subject. It can be recommended for a wide range of researchers and practitioners interested in the grey data exploration and processing.” (Zygmunt Hasiewicz, zbMATH, 1406.93002, 2019)

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