{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T22:34:29Z","timestamp":1648852469346},"reference-count":13,"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":[[2012,6]]},"abstract":"<jats:p> Let G be a finitely generated free, free abelian of arbitrary exponent, free nilpotent, or free solvable group, or a free group in the variety A<jats:sub>m<\/jats:sub>A<jats:sub>n<\/jats:sub>, and let A = {a<jats:sub>1<\/jats:sub>,\u2026, a<jats:sub>r<\/jats:sub>} be a basis for G. We prove that, in most cases, if S is a subset of a basis for G which may be expressed as a word in A without using elements from {a<jats:sub>l+1<\/jats:sub>,\u2026, a<jats:sub>r<\/jats:sub>} for some l &lt; r, then S is a subset of a basis for the relatively free group on {a<jats:sub>1<\/jats:sub>,\u2026, a<jats:sub>l<\/jats:sub>}. <\/jats:p>","DOI":"10.1142\/s0218196712500300","type":"journal-article","created":{"date-parts":[[2012,2,6]],"date-time":"2012-02-06T00:47:00Z","timestamp":1328489220000},"page":"1250030","source":"Crossref","is-referenced-by-count":0,"title":["ON RESTRICTING SUBSETS OF BASES IN RELATIVELY FREE GROUPS"],"prefix":"10.1142","volume":"22","author":[{"given":"LUCAS","family":"SABALKA","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DMYTRO","family":"SAVCHUK","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","first-page":"516","volume":"108","author":"Baumslag G.","journal-title":"Trans. Amer. Math. Soc."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1973-0330295-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1984-15246-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1992-1088442-0"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/00927879608825718"},{"key":"rf6","first-page":"513","volume":"38","author":"Gupta C. K.","journal-title":"Algebra Logic"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9964-6"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01105309"},{"key":"rf9","volume-title":"Combinatorial Group Theory","author":"Magnus W.","year":"2004"},{"key":"rf10","first-page":"996","volume":"43","author":"Roman'kov V. A.","journal-title":"Ukrain. Mat. Zh."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195127"},{"key":"rf13","first-page":"117","volume":"51","author":"Timoshenko E. I.","journal-title":"Mat. Zametki"},{"key":"rf14","first-page":"175","volume":"49","author":"Umirbaev U. U.","journal-title":"Uspekhi Mat. Nauk"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500300","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:48:24Z","timestamp":1565185704000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S0218196712500300"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500300","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}