On the commensurator of the Nottingham group

Ershov, Mikhail

doi:10.1090/S0002-9947-2010-05160-8

On the commensurator of the Nottingham group
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by Mikhail Ershov

Trans. Amer. Math. Soc. 362 (2010), 6663-6678

DOI: https://doi.org/10.1090/S0002-9947-2010-05160-8

Published electronically: August 3, 2010

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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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