{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T09:41:59Z","timestamp":1772444519850,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:p> We study type-definable subgroups of small index in definable groups, and the structure on the quotient, in first order structures. We raise some conjectures in the case where the ambient structure is o-minimal. The gist is that in this o-minimal case, any definable group G should have a smallest type-definable subgroup of bounded index, and that the quotient, when equipped with the logic topology, should be a compact Lie group of the \"right\" dimension. I give positive answers to the conjectures in the special cases when G is 1-dimensional, and when G is definably simple. <\/jats:p>","DOI":"10.1142\/s0219061304000346","type":"journal-article","created":{"date-parts":[[2005,1,14]],"date-time":"2005-01-14T11:39:54Z","timestamp":1105702794000},"page":"147-162","source":"Crossref","is-referenced-by-count":44,"title":["TYPE-DEFINABILITY, COMPACT LIE GROUPS, AND o-MINIMALITY"],"prefix":"10.1142","volume":"04","author":[{"given":"ANAND","family":"PILLAY","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana-Champaign, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf2","volume-title":"Groupes et Algebres de Lie","author":"Bourbaki N.","year":"1982"},{"key":"rf4","volume-title":"The Structure of Compact Groups","year":"1998"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/2694914"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02593-9"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02667-2"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2001.8861"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610799007528"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(88)90125-9"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90024-G"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525919"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061304000346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:31:00Z","timestamp":1565137860000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061304000346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,12]]},"references-count":10,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2004,12]]}},"alternative-id":["10.1142\/S0219061304000346"],"URL":"https:\/\/doi.org\/10.1142\/s0219061304000346","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,12]]}}}