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The subgroup growth spectrum of virtually free groups

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Abstract

For a finitely generated group Γ denote by µ(Γ) the growth coefficient of Γ, that is, the infimum over all real numbers d such that s n (Γ) < n!d. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group.

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References

  1. The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4; 2006. http://www.gap-system.org

  2. B. Huppert, Endliche Gruppen, Springer-Verlag, Berlin-Heidelberg-New York, 1967.

    MATH  Google Scholar 

  3. A. Maróti, On the orders of primitive groups, Journal of Algebra 258 (2002), 631–640.

    Article  MATH  MathSciNet  Google Scholar 

  4. T. W. Müller, Combinatorial aspects of finitely generated virtually free groups, Journal of the London Mathematical Society (2) 44 (1991), 75–94.

    Article  MATH  Google Scholar 

  5. T. W. Müller, Subgroup growth of free products, Inventiones Mathematicae 126 (1996), 111–131.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. W. Müller and J.-C. Schlage-Puchta, Character theory of symmetric groups, subgroup growth of Fuchsian groups, and random walks, Advances in Mathematics 213 (2007), 919–982.

    Article  MATH  MathSciNet  Google Scholar 

  7. T. W. Müller and J.-C. Schlage-Puchta, Decomposition of the conjugacy representation of the symmetric group, and subgroup growth, submitted.

  8. T. W. Müller and J.-C. Schlage-Puchta, Some examples in the theory of subgroup growth, Monatshefte für Mathematik 146 (2005), 49–76.

    Article  MATH  Google Scholar 

  9. T. W. Müller and J.-C. Schlage-Puchta, Some probabilistic subgruops of a finitely generated group, in preparation.

  10. J.-P. Serre, Trees, Springer-Verlag, Berlin-New York, 1980.

    MATH  Google Scholar 

  11. C. C. Sims, Primitive groups, graphs and block designs, Annals of the New York Academy of Sciences 175 (1970), 351–353.

    MATH  MathSciNet  Google Scholar 

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  1. Mathematisches Institut, Eckerstr. 1, 79104, Freiburg, Germany

    Jan-Christoph Schlage-Puchta

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  1. Jan-Christoph Schlage-Puchta
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Correspondence to Jan-Christoph Schlage-Puchta.

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Schlage-Puchta, JC. The subgroup growth spectrum of virtually free groups. Isr. J. Math. 177, 229–251 (2010). https://doi.org/10.1007/s11856-010-0044-7

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  • DOI: https://doi.org/10.1007/s11856-010-0044-7

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