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Furthermore, we prove the decidability of the two-sided Brinkmann Conjugacy Problem (2BrCP) for monomorphisms of FATF groups (and combine it with TCP) to derive the decidability of the conjugacy problem for ascending HNN extensions of FATF groups.<\/jats:p>","DOI":"10.1142\/s0219498826500027","type":"journal-article","created":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T11:51:25Z","timestamp":1723290685000},"source":"Crossref","is-referenced-by-count":1,"title":["Orbit problems for free-abelian times free groups and related families"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1585-9443","authenticated-orcid":false,"given":"Andr\u00e9","family":"Carvalho","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade do Porto, R. Campo Alegre s\/n 4169-007, Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8365-8929","authenticated-orcid":false,"given":"Jordi","family":"Delgado","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e1tiques, Universitat Polit\u00e9cnica de Catalunya, Escola Polit\u00e9cnica Superior d\u2019Enginyeria de Manresa, Av. de les Bases de Manresa, 61, 73 08242, Manresa, Barcelona"}]}],"member":"219","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"S0219498826500027BIB001","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609306018674"},{"key":"S0219498826500027BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04817-X"},{"key":"S0219498826500027BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2010.05.032"},{"key":"S0219498826500027BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S001309152200030X"},{"key":"S0219498826500027BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-024-02029-2"},{"key":"S0219498826500027BIB006","unstructured":"A. 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