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Coxeter Groups

2017
This chapter considers Coxeter groups and how to find a space on which a group acts by building a space using combinatorics from the group. It first describes groups generated by reflections, focusing on Euclidean spaces and showing that some natural, beautiful, and important subsets of Euclidean spaces have symmetric groups that are discrete and are ...
Bernhard M¨uhlherr   +2 more
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On the Efficiency of Coxeter Groups

Bulletin of the London Mathematical Society, 1997
If \(G\) is a finitely presented group and \(K\) is any \((G,2)\)-complex (that is, a finite 2-complex with fundamental group \(G\)), then it is well known that \(\chi(K)\geq 1-rk(H_1(G))+d(H_2(G))\). If equality holds for some \((G,2)\)-complex \(K\) then \(G\) is called efficient.
Baik, Y. G., Pride, S. J.
openaire   +2 more sources

Nerves of Coxeter groups

Russian Mathematical Surveys, 2003
Announcement of results.
openaire   +2 more sources

On Isomorphisms between Coxeter Groups

Designs, Codes and Cryptography, 2000
The author exhibits two non-isomorphic connected Coxeter diagrams of rank 4 (with labels 3 and \(\infty\)) such that the corresponding Coxeter groups are isomorphic. For related results compare \textit{T. Brady, J. P. McCammond, B. Mühlherr} and \textit{W. D. Neumann} [Geom. Dedicata 94, No. 1, 91-109 (2002)] and \textit{B.
openaire   +2 more sources

ON THE PROFINITE TOPOLOGY ON COXETER GROUPS

International Journal of Algebra and Computation, 2003
Using geometric methods we describe a large class of subgroups of Coxeter groups which are closed in the profinite topology and discuss some related open problems.
openaire   +1 more source

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