Regular Sets and Counting in Free Groups

  • Elizaveta Frenkel
  • Alexei G. Myasnikov
  • Vladimir N. Remeslennikov
Part of the Trends in Mathematics book series (TM)


In this paper we study asymptotic behavior of regular subsets in a free group F of finite rank, compare their sizes at infinity, and develop techniques to compute the probabilities of sets relative to distributions on F that come naturally from random walks on the Cayley graph of F. We apply these techniques to study cosets, double cosets, and Schreier representatives of finitely generated subgroups of F with an eye on complexity of algorithmic problems in free products with amalgamation and HNN extensions of groups. Mathematics Subject Classification (2000). 20E05.


Geometric group theory regular set measures on free groups Schreier transversals generic and negligible sets 


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© Springer Basel AG 2010

Authors and Affiliations

  • Elizaveta Frenkel
    • 1
  • Alexei G. Myasnikov
    • 2
  • Vladimir N. Remeslennikov
    • 3
  1. 1.MoscowRussia
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  3. 3.Omsk Branch of Mathematical Institute SB RASOmskRussia

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