Octic 2-adic fields

DOI10.1016/j.jnt.2007.12.014zbMath1140.11056OpenAlexW2011093437MaRDI QIDQ927696

David P. Roberts, John W. Jones

Publication date: 9 June 2008

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2007.12.014

zbMATH Keywords

local fields\(2\)-adic fieldsoctic extensions

Mathematics Subject Classification ID

Galois theory (11S20) Algebraic number theory computations (11Y40) Software, source code, etc. for problems pertaining to number theory (11-04) Ramification and extension theory (11S15)

Related Items (7)

DODECIC 3-ADIC FIELDS ⋮ RAMIFICATION POLYGONS, SPLITTING FIELDS, AND GALOIS GROUPS OF EISENSTEIN POLYNOMIALS ⋮ A database of local fields ⋮ Number fields unramified away from 2 ⋮ ON GALOIS p-ADIC FIELDS OF p-POWER DEGREE ⋮ Field extensions defined by power compositional polynomials ⋮ Degree 12 2-adic fields with automorphism group of order 4

Uses Software

• GAP

Cites Work

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• Dyadic exercises for octahedral extensions. II
• Galois number fields with small root discriminant
• Exercices dyadiques
• Twin sextic algebras
• Enumeration of isomorphism classes of extensions of \(p\)-adic fields.
• A database of local fields
• On the computation of all extensions of a 𝑝-adic field of a given degree
• Computation of Galois groups over function fields
• The transitive groups of degree up to eleven⁺
• Dyadic exercises for octahedral extensions
• Algorithmic Number Theory

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