{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T08:40:02Z","timestamp":1733474402722,"version":"3.30.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"name":"National Science Foundation","award":["DGE-2139899"],"award-info":[{"award-number":["DGE-2139899"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> In 1971 C. F. Miller associated to every finitely presented group G a free-by-free group [Formula: see text] known as the Miller Machine, whose conjugacy problem is closely related to the conjugacy and word problems of G. We quantify this relationship, and look to fully understand the conjugacy problem of [Formula: see text]; namely, we reduce the conjugacy problem in [Formula: see text] to a strong form of list conjugacy in G, which we term iso-computational list conjugacy. As an application, we show that if G is finite, the conjugacy problem for [Formula: see text] is in [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196724500346","type":"journal-article","created":{"date-parts":[[2024,6,29]],"date-time":"2024-06-29T06:38:26Z","timestamp":1719643106000},"page":"961-991","source":"Crossref","is-referenced-by-count":0,"title":["Conjugacy in Miller\u2019s groups"],"prefix":"10.1142","volume":"34","author":[{"given":"Conan","family":"Gillis","sequence":"first","affiliation":[{"name":"Cornell University Ithaca, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,8,14]]},"reference":[{"key":"S0218196724500346BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-10828-9_56"},{"issue":"04","key":"S0218196724500346BIB002","first-page":"964","volume":"17","author":"Borovik A.","year":"2009","journal-title":"Internat. J. Algebra Comput."},{"key":"S0218196724500346BIB003","series-title":"Advanced Courses in Mathematics \u2014 CRM Barcelona","volume-title":"The Geometry of the Word Problem for Finitely Generated Groups","author":"Brady N.","year":"2007"},{"key":"S0218196724500346BIB004","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198507727.003.0002"},{"key":"S0218196724500346BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002529"},{"key":"S0218196724500346BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2005.04.002"},{"key":"S0218196724500346BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S021819670500213X"},{"key":"S0218196724500346BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"volume-title":"Unsolved Problems in Group Theory. The Kourovka Notebook No. 18","year":"2023","author":"Mazurov V. D.","key":"S0218196724500346BIB009"},{"key":"S0218196724500346BIB010","series-title":"Annals of Mathematics Studies","volume-title":"On Group-Theoretic Decision Problems and their Classification","volume":"68","author":"Miller C.","year":"1971"},{"key":"S0218196724500346BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01556078"},{"key":"S0218196724500346BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s13373-011-0008-1"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196724500346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T08:12:48Z","timestamp":1733472768000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196724500346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,14]]},"references-count":12,"journal-issue":{"issue":"07","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["10.1142\/S0218196724500346"],"URL":"https:\/\/doi.org\/10.1142\/s0218196724500346","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2024,8,14]]}}}