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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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Relations in the maximal pro-$p$ quotients of absolute Galois groups
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by Ján Mináč, Michael Rogelstad and Nguyễn Duy Tân PDF
Trans. Amer. Math. Soc. 373 (2020), 2499-2524 Request permission

Abstract:

We observe that some fundamental constructions in Galois theory can be used to obtain interesting restrictions on the structure of Galois groups of maximal $p$-extensions of fields containing a primitive $p$-th root of unity. This is an extension of some significant ideas of Demushkin, Labute, and Serre from local fields to all fields containing a primitive $p$-th root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.
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Additional Information
  • Ján Mináč
  • Affiliation: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
  • Email: minac@uwo.ca
  • Michael Rogelstad
  • Affiliation: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
  • MR Author ID: 1162416
  • Email: mrogelst@uwo.ca
  • Nguyễn Duy Tân
  • Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam
  • Email: duytan@math.ac.vn
  • Received by editor(s): August 5, 2018
  • Received by editor(s) in revised form: February 26, 2019, and July 29, 2019
  • Published electronically: January 7, 2020
  • Additional Notes: The first-named author was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant R0370A01.
    The third-named author was partially supported by the Vietnam Academy of Science and Technology grant ĐLTE00.01/18-19.

  • Dedicated: Dedicated to John Labute
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 2499-2524
  • MSC (2010): Primary 12F10; Secondary 12E30, 20E18, 55S30
  • DOI: https://doi.org/10.1090/tran/8003
  • MathSciNet review: 4069226