{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T04:43:53Z","timestamp":1649133833458},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2016,5]]},"abstract":"<jats:p> In this paper we study a group [Formula: see text] which is the quotient of a free product of three nontrivial groups by the normal closure of a single element. In particular, we show that if the relator has length at most eight, then [Formula: see text] is nontrivial. In the case where the factors are cyclic, we prove the stronger result that at least one of the factors embeds in [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196716500223","type":"journal-article","created":{"date-parts":[[2016,4,7]],"date-time":"2016-04-07T08:41:59Z","timestamp":1460018519000},"page":"533-550","source":"Crossref","is-referenced-by-count":0,"title":["Non-triviality of some one-relator products of three groups"],"prefix":"10.1142","volume":"26","author":[{"given":"Ihechukwu","family":"Chinyere","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Physical and Applied Sciences, Michael Okpara University of Agriculture, Umudike P.M.B. 7267 Umuahia, Abia State, Nigeria"}]},{"given":"James","family":"Howie","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot\u2013Watt University, Edinburgh EH14 4AS, Scotland"}]}],"member":"219","published-online":{"date-parts":[[2016,5,29]]},"reference":[{"key":"S0218196716500223BIB001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629358.007"},{"key":"S0218196716500223BIB003","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972714000355"},{"key":"S0218196716500223BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01456216"},{"key":"S0218196716500223BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571522"},{"key":"S0218196716500223BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/00927879108824278"},{"key":"S0218196716500223BIB007","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511661860.006"},{"key":"S0218196716500223BIB008","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/53.2.271"},{"key":"S0218196716500223BIB009","series-title":"London Mathematical Society Lecture Notes Series","volume-title":"Techniques of Geometric Topology","volume":"57","author":"Fenn R. A.","year":"1983"},{"key":"S0218196716500223BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01161380"},{"key":"S0218196716500223BIB011","doi-asserted-by":"publisher","DOI":"10.4171\/055-1\/16"},{"key":"S0218196716500223BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100063969"},{"key":"S0218196716500223BIB013","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1983-0682725-0"},{"key":"S0218196716500223BIB014","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500028108"},{"key":"S0218196716500223BIB015","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-59.3.507"},{"key":"S0218196716500223BIB016","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-61.1.33"},{"key":"S0218196716500223BIB017","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-62.3.590"},{"key":"S0218196716500223BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(02)00042-7"},{"key":"S0218196716500223BIB019","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120037396"},{"key":"S0218196716500223BIB020","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1015"},{"key":"S0218196716500223BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/BF01450344"},{"key":"S0218196716500223BIB022","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1962-10868-4"},{"key":"S0218196716500223BIB024","first-page":"687","volume-title":"Group Theory from a Geometrical Viewpoint","author":"Pride S. J.","year":"1991"},{"key":"S0218196716500223BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0063195"},{"key":"S0218196716500223BIB027","doi-asserted-by":"publisher","DOI":"10.2307\/2371129"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196716500223","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:31:33Z","timestamp":1565188293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196716500223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5]]},"references-count":24,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2016,5,29]]},"published-print":{"date-parts":[[2016,5]]}},"alternative-id":["10.1142\/S0218196716500223"],"URL":"https:\/\/doi.org\/10.1142\/s0218196716500223","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5]]}}}