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Inverse Galois theory

Malle, Gunter.

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Inverse Galois theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Inverse Galois theory/ by Gunter Malle, B. Heinrich Matzat.
作者:	Malle, Gunter.
其他作者:	Matzat, B. Heinrich.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2018.,
面頁冊數:	xvii, 533 p. :digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Inverse Galois theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-662-55420-3
ISBN:	9783662554203

Inverse Galois theory
Malle, Gunter.

Inverse Galois theory[electronic resource] /by Gunter Malle, B. Heinrich Matzat. - 2nd ed. - Berlin, Heidelberg :Springer Berlin Heidelberg :2018. - xvii, 533 p. :digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

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.

ISBN: 9783662554203

Standard No.: 10.1007/978-3-662-55420-3doiSubjects--Topical Terms:

708423
Inverse Galois theory.

LC Class. No.: QA247 / .M355 2018

Dewey Class. No.: 512.32

Inverse Galois theory
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505 0 $a 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.
520 $a 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.
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