Inverse Galois Theory

Gunter Malle, B. Heinrich Matzat (Autoren)

Buch | Hardcover

XVII, 533 Seiten

2018 | 2nd ed. 2018
Springer Berlin (Verlag)
978-3-662-55419-7 (ISBN)

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This second edition addresses the question of which finite groups occur as Galois groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K, as well as its finite epimorphic images, generally referred to as the inverse problem of Galois theory.

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.

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.

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.

"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)

Erscheinungsdatum	18.09.2018
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XVII, 533 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	982 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	12F12, 12-XX, 20-XX • Braid Groups • embedding problems • Groups & group theory • Groups & group theory • Group Theory and Generalizations • Inverse Galois theory • Mathematics • mathematics and statistics • Modular Galois theory • Rigid Group generators • Topology
ISBN-10	3-662-55419-4 / 3662554194
ISBN-13	978-3-662-55419-7 / 9783662554197
Zustand	Neuware