{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T21:54:33Z","timestamp":1649022873689},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p> We study a graph related to the Andrews\u2014Curtis graph. The vertices are pairs of elements of a free group, and two vertices are adjacent if they can be obtained from one another by a left Nielsen transformation, that is, for each two words u, v the pair (u, v) is adjacent to (vu, v), (v<jats:sup>\u20111<\/jats:sup>u, v), (u, uv), and (u, u<jats:sup>\u20111<\/jats:sup>v). We study connected components of the graph and describe the shortest pairs in all components. Hence, we find a linear-time algorithm for checking whether two pairs belong to the same connected component of the graph. <\/jats:p>","DOI":"10.1142\/s0218196709005329","type":"journal-article","created":{"date-parts":[[2009,12,16]],"date-time":"2009-12-16T11:22:12Z","timestamp":1260962532000},"page":"855-871","source":"Crossref","is-referenced-by-count":0,"title":["ONE-SIDE NIELSEN TRANSFORMATIONS IN FREE GROUPS"],"prefix":"10.1142","volume":"19","author":[{"given":"ALEXEI","family":"VERNITSKI","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom, CO4 3SQ, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1965-0173241-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001468"},{"key":"rf4","doi-asserted-by":"crossref","unstructured":"M.\u00a0Coornaert, T.\u00a0Delzant and A.\u00a0Papadopoulos, G\u00e9om\u00e9trie et th\u00e9orie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov), Lecture Notes in Mathematics\u00a01441 (Springer-Verlag, Berlin, 1990)\u00a0p. 165.","DOI":"10.1007\/BFb0084913"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001365"},{"key":"rf6","unstructured":"R. C.\u00a0Lyndon and P. E.\u00a0Schupp, Classics in Mathematics (Springer, Berlin, 2001)\u00a0p. 339."},{"key":"rf8","first-page":"78","volume":"1921","author":"Nielsen J.","journal-title":"Math. Tidsskrift B"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005329","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:46:47Z","timestamp":1565185607000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005329"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":6,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.1142\/S0218196709005329"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005329","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}