Open Access
2012 Normalizers of parabolic subgroups of Coxeter groups
Daniel Allcock
Algebr. Geom. Topol. 12(2): 1137-1143 (2012). DOI: 10.2140/agt.2012.12.1137


We improve a bound of Borcherds on the virtual cohomological dimension of the nonreflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink’s result that the nonreflection part of a reflection centralizer is free. Namely, the nonreflection part of the normalizer of parabolic subgroup of type D5 or Amodd is either free or has a free subgroup of index 2.


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Daniel Allcock. "Normalizers of parabolic subgroups of Coxeter groups." Algebr. Geom. Topol. 12 (2) 1137 - 1143, 2012.


Received: 13 September 2011; Accepted: 18 January 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1248.20045
MathSciNet: MR2928907
Digital Object Identifier: 10.2140/agt.2012.12.1137

Primary: 20F55

Keywords: Coxeter group , nonreflection part , parabolic subgroup

Rights: Copyright © 2012 Mathematical Sciences Publishers

Vol.12 • No. 2 • 2012
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