Galois embedding problems with cyclic quotient of order \(p\)

DOI10.1007/BF02786686zbMath1069.12002arXivmath/0309090OpenAlexW2050177554MaRDI QIDQ1775467

Mináč, Ján, John R. Swallow

Publication date: 3 May 2005

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309090

zbMATH Keywords

Galois embedding problem

Mathematics Subject Classification ID

Galois theory (11R32) Separable extensions, Galois theory (12F10)

Related Items (13)

Construction of unipotent Galois extensions and Massey products ⋮ Four non-abelian groups of order \(p^4\) as Galois groups ⋮ Induced orthogonal representations of Galois groups ⋮ On the indecomposability of a remarkable new family of modules appearing in Galois theory ⋮ Galois module structure of square power classes for biquadratic extensions ⋮ Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel ⋮ Galois module structure of the units modulo \(p^m\) of cyclic extensions of degree \(p^n\) ⋮ A characterization of Eisenstein polynomials generating extensions of degree \(p^2\) and cyclic of degree \(p^3\) over an unramified \(\mathfrak p\)-adic field ⋮ The Sylow subgroups of the absolute Galois group \(\mathrm{Gal}(\mathbb{Q})\) ⋮ $p$-groups have unbounded realization multiplicity ⋮ Galois module structure of Galois cohomology and partial Euler-Poincaré characteristics ⋮ Automatic realization of Galois groups with cyclic quotient of order \(p^n\) ⋮ Arithmetic properties encoded in the Galois module structure of \(K^\times / K^{\times p^m}\)

Cites Work

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• Construction de p-extensions galoisiennes d'un corps de caractéristique différente de p. (Construction of Galois p-extensions of fields with characteristic different from p)
• Generic Galois extensions and problems in field theory
• Galois module structure of \(p\)th-power classes of extensions of degree \(p\)
• Groups of order 16 as Galois groups
• The Normal Closures of Certain Kummer Extensions
• On Cyclic Fields

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