%0 Journal Article
%T The pro-nilpotent group topology on a free group
%A J. Almeida
%A M. H. Shahzamanian
%A B. Steinberg
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1511.01947v1