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Galois 2-extensions unramified outside 2

✍ Scribed by John Jossey

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
187 KB
Volume
124
Category
Article
ISSN
0022-314X

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✦ Synopsis

We classify quadratic, biquadratic and degree 4 cyclic 2-rational number fields. We also classify those quadratic number fields which are not 2-rational, but have a degree 2 extension, which is Galois over Q and is 2-rational. In this case we explicitly describe the Galois group of their maximal pro-2 extension unramified outside 2 and infinity using a result of Herfort-Ribes-Zalesskii on virtually free pro-p groups.

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