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Normalizers of Parabolic Subgroups of Coxeter Groups

By Daniel Allcock

Abstract

We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection 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 non-reflection part of a reflection centralizer is free. Namely, the non-reflection part of the normalizer of parabolic subgroup of type D5 or Aodd is either free or has a free subgroup of index 2.Comment: 7 page

Topics: Mathematics - Group Theory, 20F55
Year: 2011
DOI identifier: 10.2140/agt.2012.12.1137
OAI identifier: oai:arXiv.org:1105.0253
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