Four non-abelian groups of order \(p^4\) as Galois groups

DOI10.1016/j.jalgebra.2006.05.021zbMath1171.12004OpenAlexW2111507559MaRDI QIDQ863361

Ivo M. Michailov

Publication date: 26 January 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.05.021

zbMATH Keywords

obstructionHilbert symbolGalois embedding

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Inverse Galois theory (12F12)

Related Items

On the distribution of \(\mathrm{Cl}(K)[l^\infty\) for degree \(l\) cyclic fields] ⋮ Construction of unipotent Galois extensions and Massey products ⋮ Galois realizability of groups of orders \(p^5\) and \(p^6\) ⋮ Induced orthogonal representations of Galois groups ⋮ Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel ⋮ $p$-groups have unbounded realization multiplicity ⋮ On Galois cohomology and realizability of 2-groups as Galois groups ⋮ Fields of algebraic numbers with bounded local degrees and their properties ⋮ Extensions of unipotent groups, Massey products and Galois theory ⋮ 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)
• Central \(p\)-extensions of \((p, p, \dots, p)\)-type Galois groups
• Galois embedding problems with cyclic quotient of order \(p\)
• On $p$-groups as Galois groups.
• Plongement d'une extension d'ordre p ou p2 dans une surextension non abelienne d'ordre p3.
• Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2

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