Name
Abstract | ||
|---|---|---|
We show that the following problems are decidable in a rank 2 free group F-2: 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-2? Moreover, decidability subsists if we allow H to be a rational subset of F-2, 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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1142/S0218196710005790 | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION |
Keywords | Field | DocType |
Free groups, automorphisms, orbits, f.g. subgroups, stallings' automata | Stallings theorem about ends of groups,Discrete mathematics,Outer automorphism group,Free product,Combinatorics,Automorphisms of the symmetric and alternating groups,Algebra,Automorphism,Subgroup,Mathematics,Bounded function,Free group | Journal |
Volume | Issue | ISSN |
20 | 4 | 0218-1967 |
Citations | PageRank | References |
3 | 0.50 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pedro V. Silva | 1 | 141 | 29.42 |
| Pascal Weil | 2 | 71 | 7.01 |