@article{RibesZaleski:LMS:1993,
    Abstract = {If F is a free abstract group, its profinite topology is the coarsest topology making F into a topological group, such that every group homomorphism from F into a finite group is continuous. It was shown by M. Hall Jr that every finitely generated subgroup of F is closed in that topology. Let H1, H2, {\ldots}, Hn be finitely generated subgroups of F. J.-E. Pin and C. Reutenauer have conjectured that the product H1 H2 {\ldots} Hn is a closed set in the profinite topology of F; also, they have shown that this conjecture implies a conjecture of J. Rhodes on finite semigroups. In this paper we give a positive answer to the conjecture of Pin and Reutenauer. Our method is based on the theory of profinite groups acting on graphs.},
    Author = {Ribes, Luis and Zaleski, Pavel A.},
    EPrint = {http://blms.oxfordjournals.org/content/25/1/37.full.pdf+html},
    File = {Pointlike sets the finest aperiodic cover of a finite semigroup - Henckell (0) (0) (0).pdf},
    Journal = {Bull. London Math. Soc.},
    Number = {1},
    Pages = {37--43},
    Title = {On The Profinite Topology on a Free Group},
    URL = {http://blms.oxfordjournals.org/content/25/1/37.abstract},
    Volume = {25},
    Year = {1993},
    bdsk-url-1 = {http://blms.oxfordjournals.org/content/25/1/37.abstract},
    bdsk-url-2 = {http://dx.doi.org/10.1112/blms/25.1.37},
    date-added = {2016-01-29 17:50:22 +0000},
    date-modified = {2016-01-29 17:52:14 +0000},
    doi = {10.1112/blms/25.1.37}
}

@article{RibesZaleski:LMS:1993, Abstract = {If F is a free abstract group, its profinite topology is the coarsest topology making F into a topological group, such that every group homomorphism from F into a finite group is continuous. It was shown by M. Hall Jr that every finitely generated subgroup of F is closed in that topology. Let H1, H2, {\ldots}, Hn be finitely generated subgroups of F. J.-E. Pin and C. Reutenauer have conjectured that the product H1 H2 {\ldots} Hn is a closed set in the profinite topology of F; also, they have shown that this conjecture implies a conjecture of J. Rhodes on finite semigroups. In this paper we give a positive answer to the conjecture of Pin and Reutenauer. Our method is based on the theory of profinite groups acting on graphs.}, Author = {Ribes, Luis and Zaleski, Pavel A.}, EPrint = {http://blms.oxfordjournals.org/content/25/1/37.full.pdf+html}, File = {Pointlike sets the finest aperiodic cover of a finite semigroup - Henckell (0) (0) (0).pdf}, Journal = {Bull. London Math. Soc.}, Number = {1}, Pages = {37--43}, Title = {On The Profinite Topology on a Free Group}, URL = {http://blms.oxfordjournals.org/content/25/1/37.abstract}, Volume = {25}, Year = {1993}, bdsk-url-1 = {http://blms.oxfordjournals.org/content/25/1/37.abstract}, bdsk-url-2 = {http://dx.doi.org/10.1112/blms/25.1.37}, date-added = {2016-01-29 17:50:22 +0000}, date-modified = {2016-01-29 17:52:14 +0000}, doi = {10.1112/blms/25.1.37} }