{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T02:56:19Z","timestamp":1718938579909},"reference-count":17,"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":[[2021,6]]},"abstract":"<jats:p> We prove that the conjugacy problem in the first Grigorchuk group [Formula: see text] can be solved in linear time. Furthermore, the problem to decide if a list of elements [Formula: see text] contains a pair of conjugate elements can be solved in linear time. We also show that a conjugator for a pair of conjugate element [Formula: see text] can be found in polynomial time. <\/jats:p>","DOI":"10.1142\/s0218196721500363","type":"journal-article","created":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T06:46:43Z","timestamp":1623394003000},"page":"789-806","source":"Crossref","is-referenced-by-count":1,"title":["Linear time algorithm for the conjugacy problem in the first Grigorchuk group"],"prefix":"10.1142","volume":"31","author":[{"given":"Mitra","family":"Modi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mathew","family":"Seedhom","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Ushakov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"S0218196721500363BIB001","doi-asserted-by":"publisher","DOI":"10.1155\/S1073792898000622"},{"key":"S0218196721500363BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(80)90149-0"},{"key":"S0218196721500363BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706002986"},{"key":"S0218196721500363BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(91)90074-C"},{"key":"S0218196721500363BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01078416"},{"issue":"5","key":"S0218196721500363BIB007","first-page":"939","volume":"48","author":"Grigorchuk R. I.","year":"1984","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"S0218196721500363BIB008","series-title":"Progress in Mathematics","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/3-7643-7447-0_5","volume-title":"Infinite Groups: Geometric, Combinatorial and Dynamical Aspects","volume":"248","author":"Grigorchuk R. I.","year":"2006"},{"key":"S0218196721500363BIB009","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610703004745"},{"key":"S0218196721500363BIB010","volume-title":"Topics in Geometric Group Theory","author":"de la Harpe P.","year":"2000"},{"key":"S0218196721500363BIB011","doi-asserted-by":"publisher","DOI":"10.1137\/0206024"},{"key":"S0218196721500363BIB012","doi-asserted-by":"crossref","first-page":"573","DOI":"10.4213\/mzm1432","volume":"64","author":"Leonov Y. G.","year":"1998","journal-title":"Mat. Zametki"},{"key":"S0218196721500363BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF01158402"},{"key":"S0218196721500363BIB014","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/108"},{"key":"S0218196721500363BIB015","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/348"},{"key":"S0218196721500363BIB017","first-page":"29","volume":"2","author":"Miasnikov A. G.","year":"2008","journal-title":"J. Math. Crypt."},{"key":"S0218196721500363BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-40974-8_19"},{"key":"S0218196721500363BIB019","doi-asserted-by":"crossref","first-page":"592","DOI":"10.4213\/mzm1434","volume":"64","author":"Rozhkov A. V.","year":"1998","journal-title":"Mat. Zametki"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196721500363","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,24]],"date-time":"2021-06-24T04:20:45Z","timestamp":1624508445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196721500363"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6]]},"references-count":17,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["10.1142\/S0218196721500363"],"URL":"https:\/\/doi.org\/10.1142\/s0218196721500363","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6]]}}}