{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:47:37Z","timestamp":1777423657169,"version":"3.51.4"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7954,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1992,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that a stable solvable group <jats:italic>G<\/jats:italic> which satisfies <jats:italic>x<jats:sup>n<\/jats:sup><\/jats:italic> = 1 generically is of finite exponent dividing some power of <jats:italic>n<\/jats:italic>. Furthermore, <jats:italic>G<\/jats:italic> is nilpotent-by-finile.<\/jats:p><jats:p>A second result is that in a stable group of finite exponent, involutions either have big centralisers, or invert a subgroup of finite index (which hence has to be abelian).<\/jats:p>","DOI":"10.2307\/2275290","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:44:45Z","timestamp":1146955485000},"page":"548-554","source":"Crossref","is-referenced-by-count":5,"title":["\u00c0 propos d'\u00e9quations g\u00e9n\u00e9riques"],"prefix":"10.1017","volume":"57","author":[{"given":"Frank O.","family":"Wagner","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200022830_ref014","first-page":"1026","volume":"56","author":"Wagner","year":"1991","journal-title":"Small stable groups and generics"},{"key":"S0022481200022830_ref013","unstructured":"Wagner F. O. , Stable groups and generic types, D. Phil, thesis, Oxford Uhiversity, Oxford, 1990."},{"key":"S0022481200022830_ref012","author":"Poizat","journal-title":"Sous-groupes p\u00e9riodiques d'un groupe stable"},{"key":"S0022481200022830_ref011","first-page":"131","volume-title":"Proceedings of the eighth Easter conference on model theory","author":"Poizat","year":"1990"},{"key":"S0022481200022830_ref010","volume-title":"Groupes stables","author":"Poizat","year":"1987"},{"key":"S0022481200022830_ref008","unstructured":"Hrushovski E. , Contributions to stable model theory, Ph.D. thesis, University of California, Berkeley, California, 1986."},{"key":"S0022481200022830_ref007","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1215\/ijm\/1255448649","article-title":"Some sufficient conditions for a group to be nilpotent","volume":"2","author":"Hall","year":"1958","journal-title":"Illinois Journal of Mathematics"},{"key":"S0022481200022830_ref006","first-page":"36","volume-title":"Group theory (proceedings Brixen\/Bressanone 1986","volume":"1281","author":"Hartley","year":"1987"},{"key":"S0022481200022830_ref003","first-page":"7","volume-title":"Proceedings of the sixth Easter conference on model theory","author":"Baudisch","year":"1988"},{"key":"S0022481200022830_ref001","first-page":"618","volume":"56","author":"Aguzarov","year":"1991","journal-title":"An infinite superstable group has infinitely many conjugacy classes"},{"key":"S0022481200022830_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(79)90089-9"},{"key":"S0022481200022830_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700018553"},{"key":"S0022481200022830_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(79)90284-9"},{"key":"S0022481200022830_ref009","first-page":"3","volume-title":"Group theory (proceedings, Singapore, 1987","author":"Kegel","year":"1989"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200022830","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T21:44:50Z","timestamp":1558043090000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200022830\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,6]]}},"alternative-id":["S0022481200022830"],"URL":"https:\/\/doi.org\/10.2307\/2275290","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,6]]}}}