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The embedding problem in Galois theory

Author: V V Ishkhanov; B B Lurʹe; D K Faddeev
Publisher: Providence, R.I. : American Mathematical Society, ©1997.
Series: Translations of mathematical monographs, v. 165.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The central problem of modern Galois theory involves the inverse problem: given a field k and a group G, construct an extension L/k with Galois group G. The embedding problem for fields generalizes the inverse problem and consists in finding the conditions under which one can construct a field L normal over k, with group G, such that L extends a given normal extension K/k with Galois group G/A. Moreover, the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ishkhanov, V. V. (Vladimir Vaganovich).
Embedding problem in Galois theory.
Providence, R.I. : American Mathematical Society, ©1997
(DLC) 97012187
(OCoLC)36566089
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V V Ishkhanov; B B Lurʹe; D K Faddeev
ISBN: 9781470445805 1470445808
OCLC Number: 1031952839
Description: 1 online resource.
Contents: Chapter 1. Preliminary information about the embedding problem Chapter 2. The compatibility condition Chapter 3. The embedding problem with Abelian kernel Chapter 4. The embedding problem for local fields Chapter 5. The embedding problem with non-Abelian kernel for algebraic number fields Appendix
Series Title: Translations of mathematical monographs, v. 165.
Other Titles: Zadacha pogruzhenii︠a︡ v teorii Galua.
Responsibility: V.V. Ishkhanov, B.B. Lurʹe, D.K. Faddeev ; [translated from the Russian by N.B. Lebedinskaya].

Abstract:

The central problem of modern Galois theory involves the inverse problem: given a field k and a group G, construct an extension L/k with Galois group G. The embedding problem for fields generalizes the inverse problem and consists in finding the conditions under which one can construct a field L normal over k, with group G, such that L extends a given normal extension K/k with Galois group G/A. Moreover, the requirements applied to the object L to be found are usually weakened: it is not necessary for L to be a field, but L must be a Galois algebra over the field k, with group G. In this setti.

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