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Regular Sets and Counting in Free Groups

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Combinatorial and Geometric Group Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

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.

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Author information

Authors and Affiliations

  1. Moscow, Russia

    Elizaveta Frenkel

  2. Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada

    Alexei G. Myasnikov

  3. Omsk Branch of Mathematical Institute SB RAS, 13 Pevtsova Street, Omsk, 644099, Russia

    Vladimir N. Remeslennikov

Authors
  1. Elizaveta Frenkel
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  2. Alexei G. Myasnikov
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  3. Vladimir N. Remeslennikov
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Editor information

Editors and Affiliations

  1. Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Oleg Bogopolski

  2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Inna Bumagin

  3. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St., West, Montreal, Quebec, H3A 2K6, Canada

    Olga Kharlampovich

  4. Departament de Matematica Aplicada III, EPSEM — Universitat Politècnica de Catalunya, Av. Bases de Manresa 61-73, 08242, Manresa, Barcelona, Spain

    Enric Ventura

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Frenkel, E., Myasnikov, A.G., Remeslennikov, V.N. (2010). Regular Sets and Counting in Free Groups. In: Bogopolski, O., Bumagin, I., Kharlampovich, O., Ventura, E. (eds) Combinatorial and Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9911-5_4

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