{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T23:03:44Z","timestamp":1744412624625},"reference-count":24,"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":[[2010,6]]},"abstract":"<jats:p> We show that the following problems are decidable in a rank 2 free group F<jats:sub>2<\/jats:sub>: Does a given finitely generated subgroup H contain primitive elements? And does H meet the orbit of a given word u under the action of G, the group of automorphisms of F<jats:sub>2<\/jats:sub>? Moreover, decidability subsists if we allow H to be a rational subset of F<jats:sub>2<\/jats:sub>, or alternatively if we restrict G to be a rational subset of the set of invertible substitutions (a.k.a. positive automorphisms). In higher rank, the following weaker problem is decidable: given a finitely generated subgroup H, a word u and an integer k, does H contain the image of u by some k-almost bounded automorphism? An automorphism is k-almost bounded if at most one of the letters has an image of length greater than k. <\/jats:p>","DOI":"10.1142\/s0218196710005790","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T11:00:35Z","timestamp":1278673235000},"page":"561-590","source":"Crossref","is-referenced-by-count":4,"title":["AUTOMORPHIC ORBITS IN FREE GROUPS: WORDS VERSUS SUBGROUPS"],"prefix":"10.1142","volume":"20","author":[{"given":"PEDRO V.","family":"SILVA","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, R. 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