Mathematische Zeitschrift

, Volume 250, Issue 2, pp 287–297

A constructive version of the Ribes-Zalesski product theorem


DOI: 10.1007/s00209-004-0752-y

Cite this article as:
Auinger, K. & Steinberg, B. Math. Z. (2005) 250: 287. doi:10.1007/s00209-004-0752-y


For any given finitely generated subgroups H1,...,Hn of a free group F and any element w of F not contained in the product H1Hn, a finite quotient of F is explicitly constructed which separates the element w from the set H1Hn. This provides a constructive version of the “product theorem”, stating that H1Hn 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität WienWienAustria
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada