The isomorphism problem for Coxeter groups

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By a recent result obtained by R. Howlett and the author considerable progress has been made towards a complete solution of the isomorphism problem for Coxeter groups. In this paper we give a survey on the isomorphism problem and explain in particular how the result mentioned above reduces it to its `reflection preserving' version. Furthermore we desrcibe recent developments concerning the solution of the latter.
15 pages, 0 figures, to appear in 'The Coxeter Legacy: Reflections and Projections', Fields Institute Communications

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