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As a corollary, given two conjugate elements in a [finitely generated free]-by-cyclic group, the set of conjugators can be computed and the conjugacy problem with context-free constraints is decidable. We pose several problems arising naturally from this work.<\/jats:p>","DOI":"10.1017\/s0004972724000443","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T09:03:12Z","timestamp":1717491792000},"page":"118-127","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["COMPUTING CENTRALISERS IN [FINITELY GENERATED FREE]-BY-CYCLIC GROUPS"],"prefix":"10.1017","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1585-9443","authenticated-orcid":false,"given":"ANDR\u00c9","family":"CARVALHO","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"S0004972724000443_r2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(91)90221-S"},{"volume-title":"Essays in Group Theory","year":"1987","author":"Gromov","key":"S0004972724000443_r12"},{"key":"S0004972724000443_r14","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(92)90337-F"},{"key":"S0004972724000443_r17","first-page":"1","volume-title":"Algorithms and Classification in Combinatorial Group Theory, Berkeley, CA, 1989","author":"Miller","year":"1992"},{"key":"S0004972724000443_r16","unstructured":"[16] Logan, A. 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