On Galois cohomology and realizability of 2-groups as Galois groups

DOI10.2478/s11533-011-0004-4zbMath1256.12004OpenAlexW2129051423MaRDI QIDQ539197

Ivo M. Michailov

Publication date: 27 May 2011

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-011-0004-4

zbMATH Keywords

obstructionGalois extension\(p\)-groupsquaternion algebracorestrictionEmbedding problem

Mathematics Subject Classification ID

Galois cohomology (12G05) Inverse Galois theory (12F12)

Related Items (6)

Galois realizability of groups of orders \(p^5\) and \(p^6\) ⋮ Induced orthogonal representations of Galois groups ⋮ 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 ⋮ On Galois cohomology and realizability of 2-groups as Galois groups. II ⋮ Arithmetic properties encoded in the Galois module structure of \(K^\times / K^{\times p^m}\)

Uses Software

• GAP

Cites Work

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• On 2-Groups as Galois Groups
• Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2
• Embedding obstructions for the dihedral, semidihedral, and quaternion 2-groups

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