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Equations and Fully Residually Free Groups

  • Conference paper
Combinatorial and Geometric Group Theory

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

Abstract

This paper represents notes of the mini-courses given by the authors at the GCGTA conference in Dortmund (2007), Ottawa-Saint Sauveur conference (2007), Escola d’Algebra in Rio de Janeiro (2008) and Alagna (Italy, 2008) conference on equations in groups. We explain here the Elimination process for solving equations in a free group which has Makanin-Razborov process as a prototype. We also explain how we use this process to obtain the structure theorem for finitely generated fully residually free groups and many other results.

Mini-course for the GCGTA conference in Dortmund (2007)and Escola d’Algebra in Rio de Janeiro (2008).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Burnside Hall, room 915 805 Sherbrooke West, Montreal, Quebec, Canada, H3A 2K6

    Olga Kharlampovich & Alexei G. Myasnikov

Authors
  1. Olga Kharlampovich
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  2. Alexei G. Myasnikov
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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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Kharlampovich, O., Myasnikov, A.G. (2010). Equations and Fully Residually 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_8

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