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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Wild ramification bounds and simple group Galois extensions ramified only at $ 2$


Author: John W. Jones
Journal: Proc. Amer. Math. Soc. 139 (2011), 807-821
MSC (2010): Primary 11R21, 11S15
Published electronically: August 12, 2010
MathSciNet review: 2745634
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10628-7
PII: S 0002-9939(2010)10628-7
Received by editor(s): April 2, 2010
Published electronically: August 12, 2010
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.