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

2001/10/24 by Michael R. Bush, Bush, Michael R.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0110343

arxiv created 2001/10/24 · arxiv updated 2009/12/01

Abstract

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(√(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. This is a revised version of ANT-0302.

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