A completion of some coxeter groups

  • Philippe Le Chenadec
Computational Group Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


A set of identities in Coxeter groups without commuting pairs of generators is proved confluent and well-founded. This set, possibly infinite, was intuited by experiments with the Knuth-Bendix completion procedure. An efficient algorithm for the word problem is extracted from the identities. Finally examples are given including some crystallographic groups. This case study outlines interesting features of the completion procedure, namely its ability to handle both families of groups and infinite sets of relations, from which follows the possibility to design efficient word algorithms.


Word Problem Coxeter Group Critical Pair Crystallographic Group Normal Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Philippe Le Chenadec
    • 1
  1. 1.INRIA, Domaine de VoluceauLe Chesnay CedexFrance

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