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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Wild ramification bounds and simple group Galois extensions ramified only at $2$
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by John W. Jones PDF
Proc. Amer. Math. Soc. 139 (2011), 807-821 Request permission

Abstract:

We consider finite Galois extensions of $\mathbf {Q}_p$ and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that there are no Galois extensions of $\mathbf {Q}$, unramified outside of $\{2, \infty \}$, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.
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Additional Information
  • John W. Jones
  • Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, Arizona 85287
  • Email: jj@asu.edu
  • Received by editor(s): April 2, 2010
  • Published electronically: August 12, 2010
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 807-821
  • MSC (2010): Primary 11R21, 11S15
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10628-7
  • MathSciNet review: 2745634