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On the commensurator of the Nottingham group


Author: Mikhail Ershov
Journal: Trans. Amer. Math. Soc. 362 (2010), 6663-6678
MSC (2010): Primary 20F28; Secondary 20E18, 20F40
DOI: https://doi.org/10.1090/S0002-9947-2010-05160-8
Published electronically: August 3, 2010
MathSciNet review: 2678990
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Abstract: Let $ p\geq 5$ be a prime number. We prove that the abstract commensurator of the Nottingham group $ \mathcal{N}(\mathbb{F}_p)$ coincides with its automorphism group, which is known to be a finite extension of $ \mathcal{N}(\mathbb{F}_p)$. As a corollary we deduce that the Nottingham group cannot be embedded as an open subgroup of a topologically simple group.


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Additional Information

Mikhail Ershov
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: ershov@virginia.edu

DOI: https://doi.org/10.1090/S0002-9947-2010-05160-8
Received by editor(s): October 20, 2008
Received by editor(s) in revised form: May 4, 2009
Published electronically: August 3, 2010
Additional Notes: This material is based upon work supported by the National Science Foundation under agreement No. DMS-0111298. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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