On the Galois groups of the 2-class towers of some imaginary quadratic fields

DOI10.1016/J.JNT.2006.10.016zbMath1172.11040OpenAlexW1968050989MaRDI QIDQ884534

Aliza Steurer

Publication date: 6 June 2007

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.10.016

Mathematics Subject Classification ID

Galois theory (11R32) Units and factorization (11R27)

Uses Software

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Cites Work

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• On a theorem of Koch
• Computation of Galois groups associated to the 2-class towers of some quadratic fields.
• The \(p\)-group generation algorithm
• Explicit computation of Galois \(p\)-groups unramified at \(p\)
• Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\).

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