AUTOMORPHIC ORBITS IN FREE GROUPS: WORDS VERSUS SUBGROUPS

• Tipo: Artigo em Revista Científica Internacional
• Data: 2010

Autores

Pedro V. Silva (Autor) FCUP; Pascal Weil (Autor) Outra

Revista

Título: International Journal of Algebra and Computation

Vol. 20 Nº 4

Páginas: 561-590

ISSN: 0218-1967

Editora: World Scientific

Indexação

ISI Web of Knowledge - 3 Citações

ISI Web of Science

Scopus - 6 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 30