The pro-nilpotent group topology on a free group
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 ra...
| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2017
|
| Online Access: | https://hdl.handle.net/10216/107443 |
| Country: | Portugal |
| Oai: | oai:repositorio-aberto.up.pt:10216/107443 |
| Summary: | 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. |
|---|