Computation of Galois groups associated to the 2-class towers of some quadratic fields.

DOI10.1016/S0022-314X(02)00128-2zbMath1039.11091arXivmath/0110343OpenAlexW2073321082MaRDI QIDQ1394927

Michael R. Bush

Publication date: 25 June 2003

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

Full work available at URL: https://arxiv.org/abs/math/0110343

zbMATH Keywords

class field towerideal class groupsquadratic number fields2-groups

Mathematics Subject Classification ID

Quadratic extensions (11R11) Algebraic number theory computations (11Y40) Class field theory (11R37)

Related Items (8)

Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group \(C_2 \times C_2\times C_2\) ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ Maximal unramified 3-extensions of imaginary quadratic fields and \(\text{SL}_2(\mathbb Z_3)\) ⋮ On the Galois groups of the 2-class towers of some imaginary quadratic fields ⋮ On the maximal unramified pro-2-extension over the cyclotomic \(\mathbb Z_2\)-extension of an imaginary quadratic field ⋮ On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields ⋮ 3-class field towers of exact length 3 ⋮ The 2-Class Tower of $$\mathbb {Q}(\sqrt{-5460})$$Q(-5460)

Uses Software

• KANT/KASH
• Magma

Cites Work

• Unnamed Item
• KANT V4
• Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
• On 2-class field towers of some imaginary quadratic number fields
• The \(p\)-group generation algorithm
• Explicit computation of Galois \(p\)-groups unramified at \(p\)
• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results
• Maximal unramified extensions of imaginary quadratic number fields of small conductors

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