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Groups whose geodesics are locally testable

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.

Publication metadata

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.


DOI: 10.1142/S0218196708004676


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