Automorphic orbits in free groups: words versus subgroups

Pedro Silva (1) , Pascal Weil (2)

1 CMUP - Centro de Matemática, Faculdade de Ciências
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We show that the following problems are decidable in rank 2 free groups: does a given finitely generated subgroup H contain primitive elements? and does H meet the automorphic orbit of a given word u? In higher rank, we show the decidability of the following weaker problem: 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.

Mots clés: free groups; subgroups; automorphic orbit

Domaines: Théorie des groupes [math.GR]

Pedro Silva, Pascal Weil. Automorphic orbits in free groups: words versus subgroups. 2008. ⟨hal-00324544v1⟩