Mathematische Zeitschrift

, Volume 250, Issue 2, pp 287-297

First online:

A constructive version of the Ribes-Zalesski product theorem

  • K. AuingerAffiliated withFakultät für Mathematik, Universität Wien Email author 
  • , B. SteinbergAffiliated withSchool of Mathematics and Statistics, Carleton University

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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 H1H n , a finite quotient of F is explicitly constructed which separates the element w from the set H1H n . This provides a constructive version of the “product theorem”, stating that H1H 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.