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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Abelian subgroups of pro-$p$ Galois groups
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by Antonio José Engler and Jochen Koenigsmann PDF
Trans. Amer. Math. Soc. 350 (1998), 2473-2485 Request permission

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: Fakulta̋t fűr Mathematik, Universita̋t Konstanz, Postfach 5560, D-78434 Konstanz, Germany
  • Email: jochen.koenigsmann@uni-konstanz.de
  • 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.
  • © Copyright 1998 American Mathematical Society
  • 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