{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T03:40:26Z","timestamp":1648784426204},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:p> We first introduce a loop shortening property for metric spaces, generalizing the property considered by M. Elder on Cayley graphs of finitely generated groups. Then using this metric property, we define a very broad loop shortening property for finitely generated groups. Our definition includes Elder's groups, and unlike his definition, our property is obviously a quasi-isometry invariant of the group. Furthermore, all finitely generated groups satisfying this general loop shortening property are also finitely presented and satisfy a quadratic isoperimetric inequality. Every CAT(0) cubical group is shown to have this general loop shortening property. <\/jats:p>","DOI":"10.1142\/s0218196708004883","type":"journal-article","created":{"date-parts":[[2008,12,29]],"date-time":"2008-12-29T09:49:04Z","timestamp":1230544144000},"page":"1243-1257","source":"Crossref","is-referenced-by-count":1,"title":["A QUASI-ISOMETRY INVARIANT LOOP SHORTENING PROPERTY FOR GROUPS"],"prefix":"10.1142","volume":"18","author":[{"given":"STEPHEN G.","family":"BRICK","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA"}]},{"given":"JON M.","family":"CORSON","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA"}]},{"given":"DOHYOUNG","family":"RYANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Southern Mississippi, Long Beach, MS 39560, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12494-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1999.0677"},{"key":"rf3","first-page":"1","volume":"49","author":"Corson J.","journal-title":"Glasgow Math. J."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1023\/B:GEOM.0000006500.20513.d2"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01241129"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004883","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:36:57Z","timestamp":1565185017000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004883"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12]]},"references-count":7,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,12]]}},"alternative-id":["10.1142\/S0218196708004883"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004883","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12]]}}}