{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T13:28:25Z","timestamp":1680355705044},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p> We prove that equations x<jats:sup>m<jats:sub>1<\/jats:sub><\/jats:sup> h<jats:sub>1<\/jats:sub> x<jats:sup>m<jats:sub>2<\/jats:sub><\/jats:sup> h<jats:sub>2<\/jats:sub> \u22ef x<jats:sup>m<jats:sub>k<\/jats:sub><\/jats:sup> h<jats:sub>k<\/jats:sub> over torsion-free groups are solvable when k \u2264 4. In the conclusion, we assert that the Levin question is equivalent to solving certain equations with exponent sum zero over torsion-free groups. <\/jats:p>","DOI":"10.1142\/s0218196706003013","type":"journal-article","created":{"date-parts":[[2006,4,27]],"date-time":"2006-04-27T08:53:13Z","timestamp":1146127993000},"page":"369-376","source":"Crossref","is-referenced-by-count":2,"title":["SOME EQUATIONS OVER TORSION-FREE GROUPS"],"prefix":"10.1142","volume":"16","author":[{"given":"SEONG KUN","family":"KIM","sequence":"first","affiliation":[{"name":"Department of Mathematics, Pusan National University, Pusan, South Korea 609-735, South Korea"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"227","volume":"7","author":"Baik Y. G.","journal-title":"Int. J. Algebra Comput."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500005290"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500009617"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500019283"},{"key":"rf5","first-page":"563","volume":"62","author":"Edjvet M.","journal-title":"Proc. London Math. Soc."},{"key":"rf6","doi-asserted-by":"crossref","unstructured":"S. M.\u00a0Gersten, Combinatorial Group Theory and Topology (Alta, Utah, 1984), Ann. Math. Stud.\u00a0111 (Princeton University Press, 1987)\u00a0pp. 121\u2013124.","DOI":"10.1515\/9781400882083-007"},{"key":"rf8","first-page":"165","volume":"324","author":"Howie J.","journal-title":"J. Reine Angew. Math."},{"key":"rf9","first-page":"329","volume":"3","author":"Ivanov S. V.","journal-title":"J. Group Theory"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1080\/00927879308824692"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1962-10868-4"},{"key":"rf12","doi-asserted-by":"crossref","unstructured":"R.\u00a0Lyndon, Combinatorial Group Theory and Topology (Alta, Utah, 1984), Ann. Math. Stud.\u00a0111 (Princeton University Press, 1987)\u00a0pp. 3\u201333.","DOI":"10.1515\/9781400882083-002"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.2307\/1971070"},{"key":"rf14","first-page":"145","volume":"111","author":"Stallings J. R.","journal-title":"Ann. Math. Stud."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196706003013","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:41:13Z","timestamp":1565170873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196706003013"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":13,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,4]]}},"alternative-id":["10.1142\/S0218196706003013"],"URL":"https:\/\/doi.org\/10.1142\/s0218196706003013","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]}}}