{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:15:39Z","timestamp":1770909339607,"version":"3.50.1"},"reference-count":37,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100006753","name":"Centro de Matem\u00e1tica Universidade do Porto","doi-asserted-by":"publisher","award":["UID\/MAT\/ 00144\/2013"],"award-info":[{"award-number":["UID\/MAT\/ 00144\/2013"]}],"id":[{"id":"10.13039\/501100006753","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007474","name":"Centro de Matem\u00e1tica, Universidade de Coimbra","doi-asserted-by":"publisher","award":["UID\/MAT\/00324\/2013"],"award-info":[{"award-number":["UID\/MAT\/00324\/2013"]}],"id":[{"id":"10.13039\/501100007474","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00e2ncia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BSAB\/142872\/2018"],"award-info":[{"award-number":["SFRH\/BSAB\/142872\/2018"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We give necessary and sufficient conditions for the group of a rational maximal bifix code <jats:italic>Z<\/jats:italic> to be isomorphic with the <jats:italic>F<\/jats:italic>-group of <jats:inline-formula id=\"j_forum-2018-0270_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>Z<\/m:mi>\n                              <m:mo>\u2229<\/m:mo>\n                              <m:mi>F<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_forum-2018-0270_eq_0210.png\"\/>\n                        <jats:tex-math>{Z\\cap F}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, when <jats:italic>F<\/jats:italic> is recurrent and <jats:inline-formula id=\"j_forum-2018-0270_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>Z<\/m:mi>\n                              <m:mo>\u2229<\/m:mo>\n                              <m:mi>F<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_forum-2018-0270_eq_0210.png\"\/>\n                        <jats:tex-math>{Z\\cap F}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is rational.\nThe case where <jats:italic>F<\/jats:italic> is uniformly recurrent, which is known to imply the finiteness of <jats:inline-formula id=\"j_forum-2018-0270_ineq_9997\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>Z<\/m:mi>\n                              <m:mo>\u2229<\/m:mo>\n                              <m:mi>F<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_forum-2018-0270_eq_0210.png\"\/>\n                        <jats:tex-math>{Z\\cap F}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, receives special attention.\nThe proofs are done by exploring the connections with the structure of the free profinite monoid over the alphabet of <jats:italic>F<\/jats:italic>.<\/jats:p>","DOI":"10.1515\/forum-2018-0270","type":"journal-article","created":{"date-parts":[[2019,12,21]],"date-time":"2019-12-21T09:05:31Z","timestamp":1576919131000},"page":"553-576","source":"Crossref","is-referenced-by-count":4,"title":["On the group of a rational maximal bifix code"],"prefix":"10.1515","volume":"32","author":[{"given":"Jorge","family":"Almeida","sequence":"first","affiliation":[{"name":"CMUP , Departamento de Matem\u00e1tica , Faculdade de Ci\u00eancias , Universidade do Porto , Rua do Campo Alegre 687, 4169-007 Porto , Portugal"}]},{"given":"Alfredo","family":"Costa","sequence":"additional","affiliation":[{"name":"CMUC , Department of Mathematics , University of Coimbra , Apartado 3008, EC Santa Cruz, 3001-501 Coimbra , Portugal"}]},{"given":"Revekka","family":"Kyriakoglou","sequence":"additional","affiliation":[{"name":"LIGM , Universit\u00e9 Paris-Est , Marne La Vall\u00e9e , France"}]},{"given":"Dominique","family":"Perrin","sequence":"additional","affiliation":[{"name":"LIGM , Universit\u00e9 Paris-Est , Marne La Vall\u00e9e , France"}]}],"member":"374","published-online":{"date-parts":[[2019,12,21]]},"reference":[{"key":"2023033119563197379_j_forum-2018-0270_ref_001","doi-asserted-by":"crossref","unstructured":"J.  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