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Groups whose geodesics are locally testable
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Hermiller, Susan, Holt, Derek F. and Rees, Sarah (2008) Groups whose geodesics are locally testable. International Journal of Algebra and Computation, Volume 18 (Number 5). pp. 911-923. doi:10.1142/S0218196708004676 ISSN 0218-1967.
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Abstract
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Abelian groups | ||||
Journal or Publication Title: | International Journal of Algebra and Computation | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-1967 | ||||
Official Date: | August 2008 | ||||
Dates: |
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Volume: | Volume 18 | ||||
Number: | Number 5 | ||||
Number of Pages: | 13 | ||||
Page Range: | pp. 911-923 | ||||
DOI: | 10.1142/S0218196708004676 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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