AUTOMORPHIC ORBITS IN FREE GROUPS: WORDS VERSUS SUBGROUPS

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Pedro V. Silva (Author) FCUP; Pascal Weil (Author) Other

Journal

Title: International Journal of Algebra and Computation

Vol. 20 No. 4

Pages: 561-590

ISSN: 0218-1967

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 3 Citations

ISI Web of Science

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-66V

DOI: 10.1142/s0218196710005790

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30