The computation of $\mathrm{Gal}(k^\infty /k)$ for some complex quadratic number fields $k$
Volume 212 / 2024
Acta Arithmetica 212 (2024), 71-98
MSC: Primary 11R29; Secondary 20D15
DOI: 10.4064/aa221227-25-8
Published online: 11 December 2023
Abstract
We determine $\mathrm{Gal}(k^\infty /k)$ up to isomorphism for two particular families of imaginary quadratic number fields $k$ with $2$-class field tower of length $2$, where $k^\infty $ denotes the union of the $2$-class field tower of $k$.
