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- Title
AUTOMORPHIC ORBITS IN FREE GROUPS:: WORDS VERSUS SUBGROUPS.
- Authors
SILVA, PEDRO V.; WEIL, PASCAL
- Abstract
We show that the following problems are decidable in a rank 2 free group F2: 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 F2? Moreover, decidability subsists if we allow H to be a rational subset of F2, 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.
- Subjects
ORBITS (Astronomy); AUTOMORPHISMS; LITERATURE; RINGS of integers; GROUP theory
- Publication
International Journal of Algebra & Computation, 2010, Vol 20, Issue 4, p561
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196710005790