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

The p-group generation algorithm from computational group theory is used to obtain information about large quotients of the pro-2 group G=Gal (knr,2/k) for image 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.