On 2-class field towers of imaginary quadratic number fields (Q1805357)

Let \(k\) be an imaginary quadratic number field, let \(k^1\) be its Hilbert 2-class field and \(k^2\) the Hilbert 2-class field of \(k^1\). The author studies the Galois group \(G\) of \(k^2/ k\) and is in particular interested in the case that this group is abelian or metacyclic. He determines all such cases and he describes \(G\) in terms of generators and relations.