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arXiv · 1511.01947

The pro-nilpotent group topology on a free group

J. Almeida·M. H. Shahzamanian·B. Steinberg
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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.

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J. Almeida, M. H. Shahzamanian, B. Steinberg. 2016-11-22. The pro-nilpotent group topology on a free group. https://doi.org/10.1016/j.jalgebra.2017.03.009

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