{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T20:00:51Z","timestamp":1718136051985},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p> We show that there exists no left order on the free product of two nontrivial, finitely generated, left-orderable groups such that the corresponding positive cone is represented by a regular language. Since there are orders on free groups of rank at least two with positive cone languages that are context-free (in fact, 1-counter languages), our result provides a bound on the language complexity of positive cones in free products that is the best possible within the Chomsky hierarchy. It also provides a strengthening of a result by Crist\u00f3bal Rivas which states that the positive cone in a free product of nontrivial, finitely generated, left-orderable groups cannot be finitely generated as a semigroup. As another illustration of our method, we show that the language of all geodesics (with respect to the natural generating set) that represent positive elements in a graph product of groups defined by a graph of diameter at least 3 cannot be regular. <\/jats:p>","DOI":"10.1142\/s0218196717500527","type":"journal-article","created":{"date-parts":[[2017,11,21]],"date-time":"2017-11-21T02:44:46Z","timestamp":1511232286000},"page":"1113-1120","source":"Crossref","is-referenced-by-count":5,"title":["No positive cone in a free product is regular"],"prefix":"10.1142","volume":"27","author":[{"given":"Susan","family":"Hermiller","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA"}]},{"given":"Zoran","family":"\u0160uni\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hofstra University, Hempstead, NY 11549, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,12,28]]},"reference":[{"key":"S0218196717500527BIB002","first-page":"A1188","volume":"269","author":"Benois M.","year":"1969","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"S0218196717500527BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/071\/2024640"},{"key":"S0218196717500527BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196712500373"},{"key":"S0218196717500527BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2013-06052-7"},{"key":"S0218196717500527BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1214782-4"},{"issue":"5","key":"S0218196717500527BIB007","doi-asserted-by":"crossref","first-page":"53","DOI":"10.4213\/sm564","volume":"192","author":"Dubrovina T. V.","year":"2001","journal-title":"Mat. Sb."},{"key":"S0218196717500527BIB008","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/314"},{"key":"S0218196717500527BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S021819670200122X"},{"issue":"1","key":"S0218196717500527BIB011","first-page":"69","volume":"290","author":"McCleary S. H.","year":"1985","journal-title":"Trans. Amer. Math. Soc."},{"key":"S0218196717500527BIB012","doi-asserted-by":"publisher","DOI":"10.5802\/aif.2570"},{"key":"S0218196717500527BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.10.036"},{"key":"S0218196717500527BIB014","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2000.194.209"},{"key":"S0218196717500527BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2013.07.001"},{"issue":"67","key":"S0218196717500527BIB017","first-page":"163","volume":"25","author":"Vinogradov A. A.","year":"1949","journal-title":"Mat. Sbornik N.S."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500527","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:26:23Z","timestamp":1565079983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12]]},"references-count":14,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2017,12,28]]},"published-print":{"date-parts":[[2017,12]]}},"alternative-id":["10.1142\/S0218196717500527"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500527","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12]]}}}