Realizability and automatic realizability of Galois groups of order 32

DOI10.2478/s11533-009-0072-xzbMath1256.12002OpenAlexW2002624519MaRDI QIDQ707984

Tara L. Smith, Helen G. Grundman

Publication date: 8 October 2010

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

Full work available at URL: https://doi.org/10.2478/s11533-009-0072-x

zbMATH Keywords

inverse Galois theoryquaternion algebraBrauer group2-groupsautomatic realizability

Mathematics Subject Classification ID

Inverse Galois theory (12F12)

Related Items (6)

Galois realizability of groups of orders \(p^5\) and \(p^6\) ⋮ Galois realizability of a central \(C_4\)-extension of \(D_8\) ⋮ Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel ⋮ Galois realizability of groups of order 64 ⋮ On Galois cohomology and realizability of 2-groups as Galois groups ⋮ Arithmetic properties encoded in the Galois module structure of \(K^\times / K^{\times p^m}\)

Uses Software

• GAP

Cites Work

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• Abelian extensions of arbitrary fields
• Embedding problems with cyclic kernel of order 4
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• Groups of order 16 as Galois groups
• Galois realizability of a central \(C_4\)-extension of \(D_8\)
• QUADRATIC CORESTRICTION, -EMBEDDING PROBLEMS, AND EXPLICIT CONSTRUCTION
• Extra-Special Groups of Order 32 as Galois Groups
• Automatic realizability of Galois groups of order 16
• On 2-Groups as Galois Groups
• Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf.

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