On 2-class field towers of imaginary quadratic number fields, by Franz Lemmermeyer

This paper has appeared in J. Theor. Nombres Bordeaux 6 (1994), no. 2, 261-272, and so the dvi version has been removed. Abstract. For a number field k, let k^1 denote its Hilbert 2-class field, and put k^2=(k^1)^1. We will determine all imaginary quadratic number fields k such that G = Gal(k^2/k) is abelian or metacyclic, and we will give G in terms of generators and relations. Moreover, we will correct a formula of Hasse on the 2-rank of the class group of relative quadratic extensions.

Franz Lemmermeyer <hb3@ix.urz.uni-heidelberg.de>