Computation of Galois groups associated to the 2-class towers of some quadratic fields

The $p$-group generation algorithm from computational group theory is used to obtain information about large quotients of the pro-2 group $G = $\text{Gal}$ (k^{nr,2}/k)$for$k = $\mathbb{Q}$(\sqrt{d})$with$d = -445, -1015, -1595, -2379$\mathrm{.}Ineachcaseweareabletonarrowtheidentityof$G$ down to one of a finite number of explicitly given finite groups. From this follow several results regarding the corresponding 2-class tower. This is a revised version of ANT-0302.