{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:37:18Z","timestamp":1775464638062,"version":"3.50.1"},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p> Let G=F\/r<jats:sup>F<\/jats:sup> be a group with a single defining relation, r\u2208F<jats:sub>km<\/jats:sub>\\F<jats:sub>k,m+1<\/jats:sub>, F<jats:sub>ij<\/jats:sub> the term of some polynilpotent series of the free group F. We prove: the factors of the corresponding polynilpotent series of the group G are torsion free if and only if r is not a proper power of any element of F modulo F<jats:sub>k,m+1<\/jats:sub>. We also give a description of the lower central series of a group F\/[R,R] when F\/R is a nilpotent group with torsion free lower central factors. <\/jats:p>","DOI":"10.1142\/s021819670400189x","type":"journal-article","created":{"date-parts":[[2004,8,26]],"date-time":"2004-08-26T07:56:19Z","timestamp":1093506979000},"page":"513-523","source":"Crossref","is-referenced-by-count":10,"title":["ON TORSION IN FACTORS OF POLYNILPOTENT SERIES OF A GROUP WITH A SINGLE RELATION"],"prefix":"10.1142","volume":"14","author":[{"given":"C. K.","family":"GUPTA","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. S.","family":"ROMANOVSKI","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics, Acad. Koptyug prospect 4, Novosibirsk 630090, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160130107"},{"key":"rf2","first-page":"26","volume":"13","author":"Romanovski N. S.","journal-title":"Algebra and Logic"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02801571"},{"key":"rf5","first-page":"566","volume":"9","author":"Remeslennikov V. N.","journal-title":"Algebra and Logic"},{"key":"rf6","volume":"66","author":"Gupta N.","journal-title":"Contemp. Math."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819670400189X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:40:56Z","timestamp":1565170856000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819670400189X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":5,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2004,8]]}},"alternative-id":["10.1142\/S021819670400189X"],"URL":"https:\/\/doi.org\/10.1142\/s021819670400189x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}