Algebraic & Geometric Topology

Normalizers of parabolic subgroups of Coxeter groups

Daniel Allcock

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 2 (2012), 1137-1143.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]

Coxeter group parabolic subgroup nonreflection part


Allcock, Daniel. Normalizers of parabolic subgroups of Coxeter groups. Algebr. Geom. Topol. 12 (2012), no. 2, 1137--1143. doi:10.2140/agt.2012.12.1137.

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