{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T05:05:17Z","timestamp":1648962317723},"reference-count":9,"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 n \u2265 2 be a natural number, X = { x<jats:sub>1<\/jats:sub>,\u2026, x<jats:sub>n<\/jats:sub>} and let F be the free group, freely generated by X. Let R be a cyclically reduced word in F such that its symmetric closure [Formula: see text] in F satisfies the small cancellation condition C\u2032(1\/5) &amp; T(4). Let G be the group presented by [Formula: see text]. A Magnus subsemigroup of G is any subsemigroup of G generated by at most 2n - 1 elements of [Formula: see text]. In this paper we solve the Membership Problem for rational subsets of G which are contained in a Magnus subsemigroup of G, provided that [Formula: see text] satisfies certain combinatorial conditions. We use small cancellation theory with word combinatorics. <\/jats:p>","DOI":"10.1142\/s0218196712500270","type":"journal-article","created":{"date-parts":[[2012,2,13]],"date-time":"2012-02-13T05:07:00Z","timestamp":1329109620000},"page":"1250027","source":"Crossref","is-referenced-by-count":1,"title":["SOLUTION OF THE MEMBERSHIP PROBLEM FOR CERTAIN RATIONAL SUBSETS OF ONE-RELATOR GROUPS WITH A SMALL CANCELLATION CONDITION"],"prefix":"10.1142","volume":"22","author":[{"given":"ARYE","family":"JUH\u00c1SZ","sequence":"first","affiliation":[{"name":"Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","first-page":"1188","volume":"269","author":"Benois M.","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r. A"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(00)00075-X"},{"key":"rf3","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Topics in the Theory of Group Presentations","volume":"42","author":"Johnson D. L.","year":"1982"},{"key":"rf4","first-page":"57","volume":"2","author":"Juh\u00e1sz A.","journal-title":"J. London Math. Soc."},{"key":"rf7","first-page":"239","volume":"309","author":"Kambites M.","journal-title":"J. Algebra"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.08.025"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01455888"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/372\/06879"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500270","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:48:20Z","timestamp":1565185700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":9,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S0218196712500270"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500270","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}