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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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On pro-$p$ link groups of number fields
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by Yasushi Mizusawa PDF
Trans. Amer. Math. Soc. 372 (2019), 7225-7254 Request permission


As an analogue of a link group, we consider the Galois group of the maximal pro-$p$-extension of a number field with restricted ramification which is cyclotomically ramified at $p$, i.e., tamely ramified over the intermediate cyclotomic $\mathbb Z_p$-extension of the number field. In some basic cases, such a pro-$p$ Galois group also has a Koch type presentation described by linking numbers and mod $2$ Milnor numbers (Rédei symbols) of primes. Then the pro-$2$ Fox derivative yields a calculation of Iwasawa polynomials analogous to Alexander polynomials.
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Additional Information
  • Yasushi Mizusawa
  • Affiliation: Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466-8555, Japan
  • MR Author ID: 672607
  • Email:
  • Received by editor(s): July 11, 2018
  • Received by editor(s) in revised form: December 17, 2018
  • Published electronically: February 6, 2019
  • Additional Notes: This work was supported by JSPS KAKENHI Grant Numbers JP26800010, JP17K05167.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7225-7254
  • MSC (2010): Primary 11R23; Secondary 11R18, 11R32, 57M05
  • DOI:
  • MathSciNet review: 4024552