Abstract
In this paper we determine the galois group $\operatorname{Gal}(F_1/\mathbf{Q})$ where $F_1$ is the compositum of first layers of all $\mathbf{Z}_2$-extensions over an imaginary quadratic field. Moreover, we construct $F_1$ explicitly when $k$ has class number one.
Citation
Jangheon Oh. "The first layer of $\mathbf {Z}_2^2$-extension over imaginary quadratic fields." Proc. Japan Acad. Ser. A Math. Sci. 76 (9) 132 - 134, Nov. 2000. https://doi.org/10.3792/pjaa.76.132
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