The pro-nilpotent group topology on a free group

• Tipo: Artigo em Revista Científica Internacional
• Data: 2017

Autores

Almeida, J (Autor) FCUP; Shahzamanian, MH (Autor) FCUP; Steinberg, B (Autor) Outra

Revista

Título: Journal of Algebra

Vol. 480

Páginas: 332-345

ISSN: 0021-8693

Editora: Elsevier

Indexação

ISI Web of Knowledge - 2 Citações

Scopus - 3 Citações

Outras Informações

ID Authenticus: P-00M-KMP

DOI: 10.1016/j.jalgebra.2017.03.009

Abstract (EN): In this paper, we study the pro-nilpotent group topology on a free group. First we describe the closure of the product of finitely many finitely generated subgroups of a free group in the pro-nilpotent group topology and then present an algorithm to compute it. We deduce that the nil-closure of a rational subset of a free group is an effectively constructible rational subset and hence has decidable membership. We also prove that the G(nil)-kernel of a finite monoid is computable and hence pseudovarieties of the form V (sic) G(nil) have decidable membership problem, for every decidable pseudovariety of monoids V. Finally, we prove that the semidirect product J * G(nil) has a decidable membership problem.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14