Galois module structure of square power classes for biquadratic extensions

DOI10.4153/s0008414x22000165zbMath1525.12003arXiv2105.13207OpenAlexW3164383192MaRDI QIDQ6041836

John R. Swallow, Unnamed Author, Andrew Schultz, Mináč, Ján

Publication date: 15 May 2023

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

Full work available at URL: https://arxiv.org/abs/2105.13207

zbMATH Keywords

pro-\(p\) groupsabsolute Galois groupsHilbert 90Galois moduleKlein 4-groupbiquadratic extension

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70)

Cites Work

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• 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
• On Galois cohomology and realizability of 2-groups as Galois groups. II
• Galois module structure of Milnor \(K\)-theory in characteristic \(p\)
• Galois module structure of Milnor \(K\)-theory mod \(p^s\) in characteristic \(p\)
• Automatic realization of Galois groups with cyclic quotient of order \(p^n\)
• Galois module structure of \(p\)th-power classes of extensions of degree \(p\)
• Galois embedding problems with cyclic quotient of order \(p\)
• Galois \(p\)-groups and Galois modules
• On the multiplicative group of cyclic \(p\)-extensions of a local field
• GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE pⁿ
• Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p ⁿ
• The Normal Closures of Certain Kummer Extensions
• On Cyclic Fields
• Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2
• Galois module structure of (ℓ ⁿ )th classes of fields
• $p$-groups have unbounded realization multiplicity
• Hilbert 90 for Biquadratic Extensions
• Galois module structure of Galois cohomology and partial Euler-Poincaré characteristics
• Detecting pro-p-groups that are not absolute Galois groups
• Field theory and the cohomology of some Galois groups

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