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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Reflection subgroups of Coxeter groups


Authors: Anna Felikson and Pavel Tumarkin
Journal: Trans. Amer. Math. Soc. 362 (2010), 847-858
MSC (2000): Primary 20F55, 51M20; Secondary 51F15
Published electronically: September 18, 2009
MathSciNet review: 2551508
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Abstract: We use the geometry of the Davis complex of a Coxeter group to investigate finite index reflection subgroups of Coxeter groups. The main result is the following: if $ G$ is an infinite indecomposable Coxeter group and $ H\subset G$ is a finite index reflection subgroup, then the rank of $ H$ is not less than the rank of $ G$. This generalizes earlier results of the authors (2004). We also describe the relationship between the nerves of the group and the subgroup in the case of equal rank.


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Additional Information

Anna Felikson
Affiliation: Independent University of Moscow, B. Vlassievskii 11, 119002 Moscow, Russia
Address at time of publication: Department of Mathematics, University of Fribourg, Pérolles, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
Email: felikson@mccme.ru

Pavel Tumarkin
Affiliation: Independent University of Moscow, B. Vlassievskii 11, 119002 Moscow, Russia
Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: tumarkin@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04859-4
PII: S 0002-9947(09)04859-4
Received by editor(s): January 15, 2008
Published electronically: September 18, 2009
Additional Notes: The first author was supported in part by grants NSh-5666.2006.1, INTAS YSF-06-10000014-5916, and RFBR 07-01-00390-a.
The second author was supported in part by grants NSh-5666.2006.1, MK-6290.2006.1, INTAS YSF-06-10000014-5916, and RFBR 07-01-00390-a.
Article copyright: © Copyright 2009 American Mathematical Society