Abstract.
For any given finitely generated subgroups H1,...,H n of a free group F and any element w of F not contained in the product H1⋯H n , a finite quotient of F is explicitly constructed which separates the element w from the set H1⋯H n . This provides a constructive version of the “product theorem”, stating that H1⋯H n is closed in the profinite topology of F. The method of proof also applies to other profinite topologies. It is efficient for the profinite topology as well as for the pro-p topology of F. The main tools used are universal p-extensions and inverse automata.
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The authors gratefully acknowledge support from INTAS project 99–1224. The second author was supported in part by NSERC and by the FCT and POCTI approved projects POCTI/32817/MAT/2000 and POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER.
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Auinger, K., Steinberg, B. A constructive version of the Ribes-Zalesski product theorem. Math. Z. 250, 287–297 (2005). https://doi.org/10.1007/s00209-004-0752-y
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DOI: https://doi.org/10.1007/s00209-004-0752-y