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Abelian subgroups of pro-$p$ Galois groups


Authors: Antonio José Engler and Jochen Koenigsmann
Journal: Trans. Amer. Math. Soc. 350 (1998), 2473-2485
MSC (1991): Primary 12F10; Secondary 12J20
DOI: https://doi.org/10.1090/S0002-9947-98-02063-7
MathSciNet review: 1451599
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Abstract: It is proved that non-trivial normal abelian subgroups of the Galois group of the maximal Galois $p$-extension of a field $F$ (where $p$ is an odd prime) arise from $p$-henselian valuations with non-$p$-divisible value group, provided $\# (\dot {F}/\dot {F}^{p})\geq p^{2}$ and $F$ contains a primitive $p$-th root of unity. Also, a generalization to arbitrary prime-closed Galois-extensions is given.


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Additional Information

Antonio José Engler
Affiliation: IMECC-UNICAMP, Caixa Postal 6065, 13083-970, Campinas, SP, Brasil
Email: engler@ime.unicamp.br

Jochen Koenigsmann
Affiliation: Fakultat fűr Mathematik, Universitat Konstanz, Postfach 5560, D-78434 Konstanz, Germany
Email: jochen.koenigsmann@uni-konstanz.de

DOI: https://doi.org/10.1090/S0002-9947-98-02063-7
Keywords: $p$-henselian, $p$-rigid, strongly $p$-rigid
Received by editor(s): December 20, 1995
Received by editor(s) in revised form: September 11, 1996
Additional Notes: The contents of this paper were developed while the first author enjoyed the hospitality of Konstanz University supported by GMD-CNPq.
Article copyright: © Copyright 1998 American Mathematical Society

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