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

The p-group generation algorithm from computational group theory is used to obtain information about large quotients of the pro 2-group G = Gal(k^{nr,2}/k) for k = Q(\sqrt{d}) with d = -445, -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>