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arXiv · 0705.2293

Construction of maximal unramified p-extensions with prescribed Galois groups

Manabu Ozaki
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Abstract

In the present paper, we shall show that for any prime number p, every finite p-group occurs as the Galois Group of the maximal unramified p-extension over a certain number field of finite degree. We shall also show that for any given pro-p-group G with countably many generators, there exists a number field (not necessary of finite degree) whose maximal unramified p-extension has Galois group isomorphic to G. This means that the set of the isomorphism classes of the Galois groups of the maximal unramified p-extensions over the number fields (including of infinite degree) is precisely equal to that of all the pro-p-groups with countably many generators.

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Manabu Ozaki. 2009-07-17. Construction of maximal unramified p-extensions with prescribed Galois groups. https://arxiv.org/abs/0705.2293

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