{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T20:05:16Z","timestamp":1648584316606},"reference-count":3,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,5]]},"abstract":"<jats:p> Richard Thompson's group F is nonamenable if and only if there exists a ruinous set. It is known that no three element set is ruinous. Here we explicitly construct a family of thin sets for any three element set each of whose trees has three carets. We then show where this construction fails when each of the trees has four or more carets. <\/jats:p>","DOI":"10.1142\/s0218196708004500","type":"journal-article","created":{"date-parts":[[2008,6,2]],"date-time":"2008-06-02T06:26:32Z","timestamp":1212387992000},"page":"407-419","source":"Crossref","is-referenced-by-count":2,"title":["THE RUINOUS-THIN RELATIONSHIP FOR THREE ELEMENT SETS"],"prefix":"10.1142","volume":"18","author":[{"given":"JOHN","family":"DONNELLY","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Southern Indiana, 8600 University Boulevard, Evansville, IN 47712, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"215","volume":"42","author":"Cannon J. W.","journal-title":"Enseign. Math. (2)"},{"key":"rf4","doi-asserted-by":"crossref","unstructured":"S. M.\u00a0Gersten, Selected Problems, Combinatorial Group Theory and Topology, Annals of Mathematics Studies\u00a0111, eds. S. M.\u00a0Gersten and \u00a0John Stallings (Princeton University Press, 1987)\u00a0pp. 545\u2013551.","DOI":"10.1515\/9781400882083-026"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511609589"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004500","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:27:55Z","timestamp":1565116075000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004500"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5]]},"references-count":3,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,5]]}},"alternative-id":["10.1142\/S0218196708004500"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004500","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5]]}}}