Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group \(C_2 \times C_2\times C_2\)

DOI10.1016/j.jnt.2008.06.007zbMath1177.11096OpenAlexW1986054434MaRDI QIDQ2378055

Harris Nover

Publication date: 6 January 2009

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2008.06.007

zbMATH Keywords

Galois groupsclass field towerclass groupHilbert class fieldcomplex quadratic field

Mathematics Subject Classification ID

Galois theory (11R32) Separable extensions, Galois theory (12F10) Quadratic extensions (11R11) Algebraic number theory computations (11Y40) Class field theory (11R37) Finite nilpotent groups, (p)-groups (20D15)

Related Items (4)

Grün's theorems and class groups ⋮ 3-class field towers of exact length 3 ⋮ Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$ ⋮ The 2-Class Tower of $$\mathbb {Q}(\sqrt{-5460})$$Q(-5460)

Uses Software

• Magma

Cites Work

• On a theorem of Koch
• Computation of Galois groups associated to the 2-class towers of some quadratic fields.
• Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\).
• Tamely ramified towers and discriminant bounds for number fields. II.
• The \(p\)-group generation algorithm
• Explicit computation of Galois \(p\)-groups unramified at \(p\)
• Extensions with given points of ramification
• Algorithmic Number Theory
• Unnamed Item

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