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

Michael R. Bush
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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. This is a revised version of ANT-0302.

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Michael R. Bush. 2001-10-24. Computation of Galois groups associated to the 2-class towers of some quadratic fields. https://arxiv.org/abs/math/0110343

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