The nonexistence of nonsolvable octic number fields ramified only at one small prime

DOI10.1090/S0025-5718-06-01827-8zbMath1096.11043MaRDI QIDQ5470067

Lesseni Sylla

Publication date: 29 May 2006

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

zbMATH Keywords

octic fields\(p\)-power discriminants

Mathematics Subject Classification ID

Other number fields (11R21) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29)

Related Items (7)

Nonsolvable nonic number fields ramified only at one small prime ⋮ Ramification in the inverse Galois problem ⋮ Nonsolvable number fields ramified only at 3 and 5 ⋮ Number fields unramified away from 2 ⋮ A targeted Martinet search ⋮ LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS ⋮ Wild ramification bounds and simple group Galois extensions ramified only at $2$

Uses Software

• PARI/GP

Cites Work

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• Petits discriminants des corps de nombres totalement imaginaires de degré 8. (Small discriminants of totally imaginary eight-degree number fields)
• On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields
• The minimum discriminant of totally real octic fields
• The transitive groups of degree up to eleven⁺
• Non-primitive number fields of degree eight and of signature (2,3), (4,2), and (6,1) with small discriminant
• Septic number fields which are ramified only at one small prime

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