{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:05:32Z","timestamp":1758823532191},"reference-count":25,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,5,1]],"date-time":"2012-05-01T00:00:00Z","timestamp":1335830400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct and classify all groups given by triangular presentations associated to the smallest thick generalized quadrangle that act simply transitively on the vertices of hyperbolic triangular buildings of the smallest non-trivial thickness. Our classification yields 23 non-isomorphic torsion-free groups (which were obtained in an earlier work) and 168 non-isomorphic torsion groups acting on one of two possible buildings with the smallest thick generalized quadrangle as the link of each vertex. In analogy with the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S1461157012000083_inline1\"><jats:alt-text>$\\widetilde {A}_2$<\/jats:alt-text><\/jats:inline-graphic> case, we find both torsion and torsion-free groups acting on the same building.<\/jats:p>","DOI":"10.1112\/s1461157012000083","type":"journal-article","created":{"date-parts":[[2012,5,10]],"date-time":"2012-05-10T10:19:30Z","timestamp":1336645170000},"page":"101-112","source":"Crossref","is-referenced-by-count":3,"title":["Groups acting simply transitively on vertex sets of hyperbolic triangular buildings"],"prefix":"10.1112","volume":"15","author":[{"given":"Lisa","family":"Carbone","sequence":"first","affiliation":[]},{"given":"Riikka","family":"Kangaslampi","sequence":"additional","affiliation":[]},{"given":"Alina","family":"Vdovina","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,5,1]]},"reference":[{"key":"S1461157012000083_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04689-0"},{"key":"S1461157012000083_ref5","unstructured":"[5] Carbone L. , Cartwright D. and Steger T. , Cocompact lattices in hyperbolic Kac-Moody groups, Preprint, 2006."},{"key":"S1461157012000083_ref12","unstructured":"[12] Essert J. , \u2018A geometric construction of panel-regular lattices in buildings of types $\\widetilde {A}_2$ and $\\widetilde {C}_2$ \u2019, Preprint, 2010, arXiv:0908.2713v3."},{"key":"S1461157012000083_ref16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196710005807"},{"key":"S1461157012000083_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9167-8"},{"key":"S1461157012000083_ref17","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1987-15487-5"},{"key":"S1461157012000083_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2009.11.016"},{"key":"S1461157012000083_ref13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013168623727"},{"key":"S1461157012000083_ref21","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004954009167"},{"key":"S1461157012000083_ref19","first-page":"1","article-title":"Groupes de Kac-Moody d\u00e9ploy\u00e9s et presque d\u00e9ploy\u00e9s (French) [Split and almost split Kac-Moody groups]","volume":"277","author":"R\u00e9my","year":"2002","journal-title":"Ast\u00e9risque"},{"key":"S1461157012000083_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s002090200423"},{"key":"S1461157012000083_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01265309"},{"key":"S1461157012000083_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s002090100309"},{"key":"S1461157012000083_ref20","doi-asserted-by":"publisher","DOI":"10.4171\/CMH\/49"},{"key":"S1461157012000083_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/PL00001619"},{"key":"S1461157012000083_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S014338570000016X"},{"key":"S1461157012000083_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01266618"},{"key":"S1461157012000083_ref11","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-57.2.301"},{"key":"S1461157012000083_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01266617"},{"key":"S1461157012000083_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2011.10.018"},{"key":"S1461157012000083_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s002220200224"},{"key":"S1461157012000083_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.07.019"},{"key":"S1461157012000083_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.top.2005.06.005"},{"key":"S1461157012000083_ref6","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811005130"},{"key":"S1461157012000083_ref7","doi-asserted-by":"publisher","DOI":"10.1142\/S0219199703001117"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157012000083","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:46:19Z","timestamp":1559868379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157012000083\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,1]]},"references-count":25,"alternative-id":["S1461157012000083"],"URL":"https:\/\/doi.org\/10.1112\/s1461157012000083","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5,1]]}}}