Overview
- Explores new developments in the field of Inverse Galois Theory
- Presents the most successful known existence theorems and construction methods for Galois extensions
- Introduces solutions of embedding problems combined with a collection of the existing Galois realizations
- Gives an introduction to the results on fundamental groups in positive characteristic obtained by rigid analytic methods
- Contains tables of example polynomials for transitive respectively primitive permutation groups up to degree 30
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (6 chapters)
Keywords
About this book
In the past few years, important strides have been made in all of these areas. The aim of the book is to provide a systematic and extensive overview of these advances, with special emphasis on the rigidity method and its applications. Among others, the book presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems, together with a collection of the current Galois realizations.
There have been two major developments since the first edition of this book was released. The first is the algebraization of the Katz algorithm for (linearly) rigid generating systems of finite groups; the second is the emergence of a modular Galois theory. The latter has led to new construction methods for additive polynomials with given Galois group over fields of positive characteristic. Both methods have their origin in the Galois theory of differential and difference equations.
Authors and Affiliations
About the authors
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.Bibliographic Information
Book Title: Inverse Galois Theory
Authors: Gunter Malle, B. Heinrich Matzat
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-662-55420-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2018
Hardcover ISBN: 978-3-662-55419-7Published: 14 August 2018
Softcover ISBN: 978-3-662-58555-9Published: 26 January 2019
eBook ISBN: 978-3-662-55420-3Published: 27 July 2018
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 2
Number of Pages: XVII, 533
Topics: Group Theory and Generalizations, Topology