{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T07:28:14Z","timestamp":1744270094469},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6676,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1995,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>-categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of finite Morley rank can be definable in a CM-trivial theory.<\/jats:p>","DOI":"10.2307\/2275886","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:56:55Z","timestamp":1146956215000},"page":"1251-1259","source":"Crossref","is-referenced-by-count":10,"title":["The geometry of forking and groups of finite Morley rank"],"prefix":"10.1017","volume":"60","author":[{"given":"Anand","family":"Pillay","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200018041_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90171-9"},{"key":"S0022481200018041_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90159-2"},{"key":"S0022481200018041_ref004","first-page":"768","volume":"54","author":"Corredor","year":"1989","journal-title":"Bad groups of finite Morley rank"},{"key":"S0022481200018041_ref011","volume-title":"Groupes stables","author":"Poizat","year":"1987"},{"key":"S0022481200018041_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082236"},{"key":"S0022481200018041_ref010","volume-title":"Geometrical stability theory","author":"Pillay"},{"key":"S0022481200018041_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(79)90019-6"},{"key":"S0022481200018041_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082241"},{"key":"S0022481200018041_ref001","volume-title":"Transactions of the American Mathematical Society","author":"Baudisch"},{"key":"S0022481200018041_ref002","unstructured":"Borovik A. and Poizat B. , Simple groups of finite Morley rank without nonnilpotent connected subgroups, preprint. (Russian)"},{"key":"S0022481200018041_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(09)70556-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200018041","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T20:19:14Z","timestamp":1557778754000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200018041\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["S0022481200018041"],"URL":"https:\/\/doi.org\/10.2307\/2275886","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}