Normalizers of Parabolic Subgroups of Coxeter Groups

Details Normalizers of Parabolic Subgroups of Coxeter Groups Normalizers of Parabolic Subgroups of Coxeter Groups

2011-05-02

arxiv.org/abs/1105.0253v1

Mathematics

Group Theory

7 pages

Scientific paper

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.

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