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Proceedings of the American Mathematical Society

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A remark on the structure of absolute Galois groups


Author: Tilmann Würfel
Journal: Proc. Amer. Math. Soc. 95 (1985), 353-356
MSC: Primary 12G05
DOI: https://doi.org/10.1090/S0002-9939-1985-0806069-6
MathSciNet review: 806069
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Abstract: Let the field $ F$ contain all $ p$-power roots of unity for some prime $ p$ and suppose that the absolute Galois group $ G$ of $ F$ is a one-relator pro-$ p$ group. We use Merkurjev-Suslin's theorem on the power norm residue symbol to show that $ G$ is an extension of a Demushkin group by a free pro-$ p$ group.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Merkur'ev and A. A. Suslin, $ K$-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR-Izv. 21 (1983), 307-340. MR 675529 (84i:12007)
  • [2] J-P. Serre, Structure de certains pro-$ p$ groupes, Séminaire Bourbaki 1962/63, exposé no. 252.
  • [3] -, Corps locaux, Hermann, Paris, 1968. MR 0354618 (50:7096)

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DOI: https://doi.org/10.1090/S0002-9939-1985-0806069-6
Article copyright: © Copyright 1985 American Mathematical Society

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