The pro-nilpotent group topology on a free group

• Type: Article in International Scientific Journal
• Date: 2017

Authors

Almeida, J (Author) FCUP; Shahzamanian, MH (Author) FCUP; Steinberg, B (Author) Other

Journal

Title: Journal of Algebra

Vol. 480

Pages: 332-345

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 3 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14