The pro-nilpotent group topology on a free group
Group Theory
2017-03-24 v2
Abstract
In this paper, we work on the pro-nilpotent group topology of a free group. First we investigate the closure of the product of finitely many subgroups of a free group in the pro-nilpotent group topology. We present an algorithm for the calculation of the closure in the pro-nilpotent group topology of the product of finitely many finitely generated subgroups of a free group. Then we deduce that the nil-closure of a rational subset is computable. We also prove that the pseudovarieties V malcev G_nil, for every decidable pseudovariety of monoids V, and J * G_nil are decidable.
Keywords
Cite
@article{arxiv.1511.01947,
title = {The pro-nilpotent group topology on a free group},
author = {J. Almeida and M. H. Shahzamanian and B. Steinberg},
journal= {arXiv preprint arXiv:1511.01947},
year = {2017}
}
Comments
Restructured following, in part, suggestions of the referee