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IJAC
2010

Automorphic orbits in Free Groups: Words versus Subgroups

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Automorphic orbits in Free Groups: Words versus Subgroups
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.
Pedro V. Silva, Pascal Weil
Added 27 Jan 2011
Updated 27 Jan 2011
Type Journal
Year 2010
Where IJAC
Authors Pedro V. Silva, Pascal Weil
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