Israel Journal of Mathematics

, Volume 85, Issue 1–3, pp 391–405 | Cite as

Brauer groups, embedding problems, and nilpotent groups as Galois groups

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Abstract

Let ℚ ab denote the maximal abelian extension of the rationals ℚ, and let ℚabnil denote the maximal nilpotent extension of ℚ ab . We prove that for every primep, the free pro-p group on countably many generators is realizable as the Galois group of a regular extension of ℚabnil(t). We also prove that ℚabnil is not PAC (pseudo-algebraically closed).

Keywords

Galois Group Solution Field Proper Solution Embedding Problem Profinite Group 
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Copyright information

© Hebrew University 1994

Authors and Affiliations

  1. 1.Technion—Israel Institute of TechnologyHaifaIsrael

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