Computation of Galois groups associated to the 2-class towers of some quadratic fields, by Michael R. Bush

Abstract: 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 $d = -445, -1015, -1595, -2379$. In each case we are able to narrow the identity of $G$ down to one of a finite number of explicitly given finite groups. From this follow several results regarding the corresponding 2-class tower.

Michael R. Bush <mrbush@math.uiuc.edu>