The imaginary abelian number fields of 2-power degrees with ideal class groups of exponent ≤2

Ahn, Jeoung-Hwan; Kwon, Soun-Hi

doi:10.1090/S0025-5718-2011-02509-3

The imaginary abelian number fields of $2$-power degrees with ideal class groups of exponent $\leq 2$
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by Jeoung-Hwan Ahn and Soun-Hi Kwon;

Math. Comp. 81 (2012), 533-554

DOI: https://doi.org/10.1090/S0025-5718-2011-02509-3

Published electronically: July 1, 2011

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Abstract:

In this paper, assuming the Generalized Riemann Hypothesis, we determine all imaginary abelian number fields $N$ of 2-power degrees with ideal class groups of exponents $\le 2$ for which the 2-ranks of the Galois group of $N$ over $\mathbb {Q}$ are equal to 2.

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