{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T05:40:13Z","timestamp":1648964413240},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p> We give criteria for determining the approximate length of elements in any given cyclic subgroup of the Thompson\u2013Stein groups F(n<jats:sub>1<\/jats:sub>,\u2026,n<jats:sub>k<\/jats:sub>) such that n<jats:sub>1<\/jats:sub> - 1|n<jats:sub>i<\/jats:sub> - 1 \u2200i \u2208 {1,\u2026,k} in terms of the number of leaves in the minimal tree-pair diagram representative. This leads directly to the result that cyclic subgroups are quasi-isometrically embedded in the Thompson\u2013Stein groups. This result also leads to the corollaries that \u2124<jats:sup>n<\/jats:sup> is also quasi-isometrically embedded in the Thompson\u2013Stein groups for all n \u2208 \u2115 and that the Thompson\u2013Stein groups have infinite dimensional asymptotic cone. <\/jats:p>","DOI":"10.1142\/s0218196711006212","type":"journal-article","created":{"date-parts":[[2011,4,6]],"date-time":"2011-04-06T12:14:25Z","timestamp":1302092065000},"page":"365-385","source":"Crossref","is-referenced-by-count":0,"title":["CYCLIC SUBGROUPS ARE QUASI-ISOMETRICALLY EMBEDDED IN THE THOMPSON\u2013STEIN GROUPS"],"prefix":"10.1142","volume":"21","author":[{"given":"CLAIRE","family":"WLADIS","sequence":"first","affiliation":[{"name":"Department of Mathematics, Borough of Manhattan Community College, City University of New York, 199 Chambers St., New York, NY 10007, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7315"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-100106774"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(87)90015-6"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388451"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610799007127"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7618"},{"key":"rf8","first-page":"215","volume":"42","author":"Cannon J. W.","journal-title":"Enseign. Math."},{"key":"rf9","first-page":"141","volume":"9","author":"Cleary S.","journal-title":"New York J. Math."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.4213\/sm419"},{"key":"rf12","volume":"130","author":"Guba V.","journal-title":"Mem. Amer. Math. Soc."},{"key":"rf13","volume":"8","author":"Higman G.","journal-title":"Notes on Pure Math."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1094555-4"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196711006212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:22:13Z","timestamp":1565130133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196711006212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2]]},"references-count":12,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2011,2]]}},"alternative-id":["10.1142\/S0218196711006212"],"URL":"https:\/\/doi.org\/10.1142\/s0218196711006212","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2]]}}}