On 3-Class groups of certain pure cubic fields

DOI10.1017/S0004972700035292zbMath1159.11043MaRDI QIDQ5472703

Frank III Gerth

Publication date: 12 June 2006

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

class groupspure cubic fields

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items (12)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ 5-rank of ambiguous class groups of quintic Kummer extensions ⋮ l-Class groups of cyclic extensions of prime degree l ⋮ The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$ ⋮ 3-Principalization over S3 -fields ⋮ On the 3-rank of tame kernels of certain pure cubic number fields ⋮ 3-rank of ambiguous class groups of cubic Kummer extensions ⋮ On a conjecture of Lemmermeyer ⋮ 3-Class groups of cubic cyclic function fields ⋮ Fields ℚ(d3,ζ3) whose 3-class group is of type (9,3) ⋮ The 3-class groups of \(\mathbb{Q}(\sqrt[3{p})\) and its normal closure] ⋮ \(\ell\)-class groups of fields in Kummer towers

Cites Work

• On the ramification of Hecke algebras at Eisenstein primes
• Remarks on principal factors in a relative cubic field
• Pure cubic fields whose class numbers are multiples of three
• A Computational Technique for Determining the Class Number of a Pure Cubic Field

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