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Lookup NU author(s): Professor Sarah Rees
A regular set of words is (k-)locally testable if membership of a word in the set is determined by the nature of its subwords of some bounded length k. In this article we study groups for which the set of all geodesic words with respect to some generating set is (k-)locally testable, and we call such groups (k-)locally testable. We show that a group is 1-locally testable if and only if it is free abelian. We show that the class of (k-)locally testable groups is closed under taking finite direct products. We show also that a locally testable group has finitely many conjugacy classes of torsion elements. Our work involved computer investigations of specific groups, for which purpose we implemented an algorithm in GAP to compute a finite state automaton with language equal to the set of all geodesics of a group (assuming that this language is regular), starting from a shortlex automatic structure. We provide a brief description of that algorithm. © 2008 World Scientific Publishing Company.
Author(s): Hermiller S, Holt D, Rees SE
Publication type: Article
Publication status: Published
Journal: International Journal of Algebra and Computation
Year: 2008
Volume: 18
Issue: 5
Pages: 911-923
Print publication date: 01/08/2008
ISSN (print): 0218-1967
ISSN (electronic): 1793-6500
Publisher: World Scientific Publishing Co.
URL: http://dx.doi.org/10.1142/S0218196708004676
DOI: 10.1142/S0218196708004676
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