{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T17:56:44Z","timestamp":1649095004714},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,8]]},"abstract":"<jats:p> 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. <\/jats:p><jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0218196708004676","type":"journal-article","created":{"date-parts":[[2008,8,25]],"date-time":"2008-08-25T05:25:17Z","timestamp":1219641917000},"page":"911-923","source":"Crossref","is-referenced-by-count":2,"title":["GROUPS WHOSE GEODESICS ARE LOCALLY TESTABLE"],"prefix":"10.1142","volume":"18","author":[{"given":"SUSAN","family":"HERMILLER","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Nebraska, Lincoln NE 68588-0130, USA"}]},{"given":"DEREK F.","family":"HOLT","sequence":"additional","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK"}]},{"given":"SARAH","family":"REES","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Newcastle, Newcastle NE1 7RU, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(73)80005-6"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-004-0666-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196701000619"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-007-2206-3"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196707003603"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035216"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003360"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01761708"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01241129"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-2215-3"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8594-1"},{"key":"rf16","series-title":"Fundamental Studies in Computer Science","volume-title":"Finite Automata. Behavior and Synthesis","volume":"1","author":"Trakhtenbrot B. A.","year":"1973"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196799000035"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004676","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:28:25Z","timestamp":1565116105000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004676"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8]]},"references-count":14,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,8]]}},"alternative-id":["10.1142\/S0218196708004676"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004676","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8]]}}}