Geodesic rewriting systems and pregroups

Volker Diekert, Andrew J. Duncan, Alexei G. Myasnikov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

12 Scopus citations

Abstract

In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent and then systems in which the length reducing rules lead to geodesics. Combining these properties we arrive at our main object of study which we call geodesically perfect rewriting systems. We show that these are well behaved and convenient to use, and give several examples of classes of groups for which they can be constructed from natural presentations. We describe a Knuth-Bendix completion process to construct such systems, show how they may be found with the help of Stallings' pregroups and conversely may be used to construct such pregroups.

Original languageEnglish
Title of host publicationCombinatorial and Geometric Group Theory
EditorsOleg Bogopolski, Inna Bumagin, Olga Kharlampovich, Enric Ventura
Pages55-91
Number of pages37
DOIs
StatePublished - 2010
EventInternational Conference on Combinatorial and Geometric Group Theory with Applications, GAGTA 2007 - Dortmund, Germany
Duration: 27 Aug 200731 Aug 2007

Publication series

NameTrends in Mathematics
Volume47
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

ConferenceInternational Conference on Combinatorial and Geometric Group Theory with Applications, GAGTA 2007
Country/TerritoryGermany
CityDortmund
Period27/08/0731/08/07

Keywords

  • Geodesically Perfect
  • Knuth-Bendix
  • Stallings pregroups
  • String rewriting systems

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