LEADER 03111nam  22005055  450 
001 9910300133503321
005 20230913194319.0
010   $a3-662-55420-8
024 7 $a10.1007/978-3-662-55420-3
035   $a(CKB)4100000005323339
035   $a(DE-He213)978-3-662-55420-3
035   $a(MiAaPQ)EBC5477788
035   $a(PPN)229501214
035   $a(EXLCZ)994100000005323339
100   $a20180727d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aInverse Galois Theory /$fby Gunter Malle, B. Heinrich Matzat
205   $a2nd ed. 2018.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2018.
215   $a1 online resource (XVII, 533 p.) 
225 1 $aSpringer Monographs in Mathematics,$x2196-9922
311   $a3-662-55419-4 
320   $aIncludes bibliographical references and index.
327   $aI.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.
330   $aThis second edition addresses the question of which finite groups occur as Galois groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K, as well as its finite epimorphic images, generally referred to as the inverse problem of Galois theory. In the past few years, important strides have been made in all of these areas. The aim of the book is to provide a systematic and extensive overview of these advances, with special emphasis on the rigidity method and its applications. Among others, the book presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems, together with a collection of the current Galois realizations. There have been two major developments since the first edition of this book was released. The first is the algebraization of the Katz algorithm for (linearly) rigid generating systems of finite groups; the second is the emergence of a modular Galois theory. The latter has led to new construction methods for additive polynomials with given Galois group over fields of positive characteristic. Both methods have their origin in the Galois theory of differential and difference equations.
410  0$aSpringer Monographs in Mathematics,$x2196-9922
606   $aGroup theory
606   $aTopology
606   $aGroup Theory and Generalizations
606   $aTopology
615  0$aGroup theory.
615  0$aTopology.
615 14$aGroup Theory and Generalizations.
615 24$aTopology.
676   $a512.2
700   $aMalle$b Gunter$4aut$4http://id.loc.gov/vocabulary/relators/aut$0513899
702   $aMatzat$b B. Heinrich$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910300133503321
996   $aInverse Galois Theory$92000201
997   $aUNINA