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Generating Tuples of Virtually Free Groups

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Combinatorial and Geometric Group Theory

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

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Abstract

We give a complete description of all generating tuples of a virtually free group, i.e., we give a parametrization of Epi(Fn, Г) where n ∈ N and G is a virtually free group.

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References

  1. M.J. Dunwoody Folding sequences Geometry & Topology Monographs. Volume 1: The Epstein Birthday Schrift, 139, 158.

    Google Scholar 

  2. T. Delzant, Sous-groupes à deux générateurs des groupes hyperboliques. E. Ghys, A. Haefliger and A. erjovski (ed.) et al., Group theory from a geometrical viewpoint. Singapore: World Scientific., 1991, 177–189.

    Google Scholar 

  3. M. Heusener and R. Weidmann, Generating Pairs of 2-Bridge knot groups, to appear in Geom. Ded.

    Google Scholar 

  4. I. Kapovich and R. Weidmann, Freely indecomposable groups acting on hyperbolic spaces, IJAC 14 (2004), 115–171.

    MATH  MathSciNet  Google Scholar 

  5. I. Kapovich and R. Weidmann, Kleinian groups and the rank problem, Geometry and Topology 9 (2005), 375–402.

    Article  MATH  MathSciNet  Google Scholar 

  6. I. Kapovich, A. Myasnikov and R. Weidmann. A-graphs, foldings and the induced splittings IJAC 15 no.1, 2005, 95–128.

    MATH  MathSciNet  Google Scholar 

  7. O. Kharlampovich and M. Myasnikov, Irreducible Affine Varieties over a free group, J. Algebra 200, 1998, 517–570.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Karrass, A. Pietrowski and D. Solitar, Finite and infinite cyclic extensions of free groups. Collection of articles dedicated to the memory of Hanna Neumann IV., J. Austral. Math. Soc. 16, 1973, 458–466.

    Article  MATH  MathSciNet  Google Scholar 

  9. P.A. Linnell, On accessibility of groups J. Pure Appl. Algebra 30, 1983, 39–46.

    Article  MATH  MathSciNet  Google Scholar 

  10. A.I. Malcev, On isomorphic representations of infinite groups by matrices Mat. Sb. 8, 1940, 405–422.

    MathSciNet  Google Scholar 

  11. J. Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78, 1917, 385–397.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Nielsen, Om Regning med ikke kommutative Faktorer og dens Anvendlese i Gruppenteorien, Mat. Tidskrift B, 1921, 77–94.

    Google Scholar 

  13. M.R. Pettet, Virtually free groups with finitely many outer automorphisms, Trans. AMS 349, no. 10, 1997, 4565–4587.

    Article  MATH  MathSciNet  Google Scholar 

  14. A.A. Razborov, On systems of Equations in a Free Group, PhD thesis, Steklov Math. Inst., 1987.

    Google Scholar 

  15. G.P. Scott The geometries of 3-manifolds Bull. Lond. Math. Soc. 15, 1983, 401–487.

    Article  MATH  Google Scholar 

  16. Z. Sela, Diophantine geometry over groups I. Makanin Razborov Diagrams. Publ. Math. IHES 93, 2001, 31–105.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Stallings, Groups of cohomological dimension one. Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVIII, New York, 1968), 1970, 124–128.

    MathSciNet  Google Scholar 

  18. R. Weidmann, On accessibility of finitely generated groups, to appear in Q. J. Math.

    Google Scholar 

  19. H. Zieschang, Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam, Inv.Math. 10, 4–37, 1970.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Heriot Watt-University, Riccarton, Edinburgh, EH14 4AS, UK

    Richard Weidmann

Authors
  1. Richard Weidmann
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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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Weidmann, R. (2010). Generating Tuples of Virtually 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_13

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