3-Principalization over S3 -fields

DOI10.3906/mat-2103-58zbMath1497.11275arXiv2103.04184OpenAlexW3201118853MaRDI QIDQ5099155

Daniel C. Mayer, S. Aouissi, Moulay Chrif Ismaili, Mohammed Talbi

Publication date: 31 August 2022

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.04184

zbMATH Keywords

presentationscapitulationpure cubic fieldsGalois actionrelation rankfinite 3-groups\(p\)-group generation algorithmdescendant treesmaximal unramified pro-3-extensionpure metacyclic \(S_3\)-fields

Mathematics Subject Classification ID

Galois theory (11R32) Generators, relations, and presentations of groups (20F05) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Finite nilpotent groups, (p)-groups (20D15) Other abelian and metabelian extensions (11R20)

Related Items (1)

Structure of relative genus fields of cubic Kummer extensions

Cites Work

• 3-class field towers of exact length 3
• On 3-class groups of cyclic cubic extensions of certain number fields
• On the ramification of Hecke algebras at Eisenstein primes
• 3-rank of ambiguous class groups of cubic Kummer extensions
• A principal ideal theorem in the genus field
• New number fields with known p-class tower
• On 3-class groups of pure cubic fields.
• A computer aided classification of certain groups of prime power order
• The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$
• Fields ℚ(d3,ζ3) whose 3-class group is of type (9,3)
• On 3-Class groups of certain pure cubic fields
• A remark concerning Hilbert's Theorem 94.
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