Titlebook: Inverse Galois Theory; Gunter Malle,B. Heinrich Matzat Book 2018Latest edition Springer-Verlag GmbH Germany, part of Springer Nature 2018

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Embedding Problems,The question of whether a given Galois extension can be embedded into a larger one is called an embedding problem.

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Additive Polynomials,In this chapter we construct polynomials with prescribed Galois group in positive characterisic.

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Rigid Analytic Methods,The solution of the inverse problem of Galois theory over the field C.t / was achieved by a blend of topological and analytical methods.

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Action of Braids,itz (1891), goes back to results of Fried (1977, 1984) and Fried and Biggers (1982). A variant more suitable for the realization of groups as Galois groups was proposed by Matzat (1989) and subsequently developed in papers of Matzat (1991a) and in geometric context, of Fried and Voolklein (1991) (see also the survey article Matzat (1991c)).

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Gunter Malle,B. Heinrich MatzatExplores 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 p

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Springer Monographs in Mathematicshttp://image.papertrans.cn/i/image/474664.jpg

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https://doi.org/10.1007/978-3-662-55420-312F12, 12-XX, 20-XX; Inverse Galois theory; Rigid Group generators; Braid groups; Embedding problems; Mod

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1439-7382 ds for Galois extensions.Introduces solutions of embedding pThis 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 it