{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T05:16:29Z","timestamp":1648790189797},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p> We give an example of a Cayley graph [Formula: see text] for the group [Formula: see text] which is not minimally almost convex (MAC). On the other hand, the standard Cayley graph for [Formula: see text] does satisfy the falsification by fellow traveler property (FFTP), which is strictly stronger. As a result, any Cayley graph property [Formula: see text] lying between FFTP and MAC (i.e., [Formula: see text]) is dependent on the generating set. This includes the well-known properties FFTP and almost convexity, which were already known to depend on the generating set as well as Po\u00e9naru\u2019s condition [Formula: see text] and the basepoint loop shortening property (LSP) for which dependence on the generating set was previously unknown. We also show that the Cayley graph [Formula: see text] does not have the LSP, so this property also depends on the generating set. <\/jats:p>","DOI":"10.1142\/s0218196722500059","type":"journal-article","created":{"date-parts":[[2021,10,30]],"date-time":"2021-10-30T16:42:33Z","timestamp":1635612153000},"page":"115-126","source":"Crossref","is-referenced-by-count":0,"title":["A Cayley graph for F2 \u00d7 F2 which is not minimally almost convex"],"prefix":"10.1142","volume":"32","author":[{"given":"Andrew","family":"Elvey Price","sequence":"first","affiliation":[{"name":"CNRS, Institut Denis Poisson, Universit\u00e9 de Tours, Parc Grandmont, 37200 Tours, France"}]}],"member":"219","published-online":{"date-parts":[[2021,10,30]]},"reference":[{"key":"S0218196722500059BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181266"},{"key":"S0218196722500059BIB002","doi-asserted-by":"publisher","DOI":"10.1023\/B:GEOM.0000006500.20513.d2"},{"key":"S0218196722500059BIB003","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2005.5.129"},{"key":"S0218196722500059BIB004","doi-asserted-by":"publisher","DOI":"10.1515\/jgth.2005.8.2.239"},{"key":"S0218196722500059BIB005","doi-asserted-by":"publisher","DOI":"10.1515\/gcc-2013-0001"},{"issue":"1","key":"S0218196722500059BIB006","first-page":"119","volume":"5","author":"Kapovich I.","year":"2002","journal-title":"J. Group Theory"},{"key":"S0218196722500059BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"S0218196722500059BIB008","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005025418287"},{"key":"S0218196722500059BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01241129"},{"key":"S0218196722500059BIB011","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214447807"},{"key":"S0218196722500059BIB012","volume-title":"Zur fast-Konvexit\u00e4t einiger Nilpotenter Gruppen","author":"Thiel C.","year":"1992"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196722500059","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T10:48:07Z","timestamp":1644576487000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196722500059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,30]]},"references-count":11,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["10.1142\/S0218196722500059"],"URL":"https:\/\/doi.org\/10.1142\/s0218196722500059","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,30]]}}}