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On the commensurator of the Nottingham group
Author(s):
Mikhail
Ershov
Journal:
Trans. Amer. Math. Soc.
362
(2010),
6663-6678.
MSC (2010):
Primary 20F28;
Secondary 20E18, 20F40
Posted:
August 3, 2010
MathSciNet review:
2678990
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Additional information
Abstract:
Let  be a prime number. We prove that the abstract commensurator of the Nottingham group  coincides with its automorphism group, which is known to be a finite extension of  . As a corollary we deduce that the Nottingham group cannot be embedded as an open subgroup of a topologically simple group.
References:
-
- [Ab]
- A. G. Abercrombie, Subgroups and subrings of profinite rings, Math. Proc. Cambridge Philos. Soc. 116 (1994), no. 2, 209-222. MR 1281541 (95h:11078)
- [AV]
- M. Abert and B. Virag, Dimension and randomness in groups acting on rooted trees, J. Amer. Math. Soc. 18 (2005), no. 1, 157-192. MR 2114819 (2005m:20058)
- [BEW]
- Y. Barnea, M. Ershov and T. Weigel, Abstract commensurators of profinite groups,
to appear in Transactions of the AMS. - [BGJMS]
- Y. Barnea, N. Gavioli, A. Jaikin-Zapirain, V. Monti and C. M. Scoppola, Pro-
 groups with few normal subgroups, J. Algebra 321 (2009), no. 2, 429-449. MR 2483275 - [BK]
- Y. Barnea and B. Klopsch, Index subgroups of the Nottingham group, Adv. Math. 180 (2003), 187-221. MR 2019222 (2004m:20054)
- [BSh]
- Y. Barnea and A. Shalev, Hausdorff dimension, pro-
 groups, and Kac-Moody algebras, Trans. Amer. Math. Soc. 349 (1997), no. 12, 5073-5091. MR 1422889 (98b:20041) - [BShZ]
- Y. Barnea, A. Shalev and E. I. Zelmanov, Graded subalgebras of affine Kac-Moody algebras, Israel J. Math. 104 (1998), 321-334. MR 1622319 (99d:17025)
- [Ca]
- R. Camina, The Nottingham group, New horizons in pro-
 groups, 205-221, Progr. Math., 184, Birkhäuser Boston, Boston, MA, 2000. MR 1765121 (2001f:20054) - [Er]
- M. Ershov, New just-infinite pro-
 groups of finite width and subgroups of the Nottingham group, J. Algebra 275 (2004), no. 1, 419-449. MR 2047455 (2005b:20052) - [K]
- B. Klopsch, Automorphisms of the Nottingham group, J. Algebra 223 (2000), no. 1, 37-56. MR 1738250 (2000j:20047)
- [Pi]
- R. Pink, Compact subgroups of linear algebraic groups, J. Algebra 206 (1998), no. 2, 438-504. MR 1637068 (99g:20087)
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Additional Information:
Mikhail
Ershov
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email:
ershov@virginia.edu
DOI:
10.1090/S0002-9947-2010-05160-8
PII:
S 0002-9947(2010)05160-8
Received by editor(s):
October 20, 2008
Received by editor(s) in revised form:
May 4, 2009
Posted:
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
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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