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# Local recognition of reflection graphs on Coxeter groups

Local recognition of reflection graphs on Coxeter groups
Armin Straub — Diploma Thesis (TU Darmstadt) — supervisor: Ralf Köhl (né Gramlich) — 2008

## Abstract

We provide local recognition results for the reflection graphs on spherical Coxeter groups. In particular, we study the case $$F_4$$ which is locally recognizable under additional constraints only. It is then demonstrated in the cases $$A_n$$ and $$F_4$$ how these graph theoretical recognition results can be used to characterize the corresponding Coxeter groups in terms of their reflection centralizers. Finally, we outline the connection to the local recognition of Chevalley groups which is particularly important in the classification of the finite simple groups.

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807.21 KB Diploma thesis as submitted at TU Darmstadt with minor corrections (PDF, 93 pages) 2005

## BibTeX

@article{diploma-2008,
author = {Armin Straub},
title = {Local recognition of reflection graphs on {C}oxeter groups},
journal = {Diploma Thesis (TU Darmstadt)},
year = {2008},
}