Advertisement

Journal of Mathematical Sciences

, Volume 186, Issue 3, pp 387–393 | Cite as

The number of finite index subgroups of Baumslag–Solitar groups

  • V. A. Churkin
  • F. A. Dudkin
Article
  • 59 Downloads

Gelman obtained a simple formula for the number of finite index subgroups of Baumslag–Solitar groups BS(p, q) = 〈a, t | t −1 a p t = a q 〉, where p and q are coprime integers. We generalize this formula to the case of arbitrary nonzero integers. The proof is obtained by calculating the number of permutations yS n such that the subgroup of S n generated by x and y, where x is given, is transitive. Bibliography: 4 titles.

Keywords

Great Common Divisor Canonical Decomposition Great Common Divisor Coprime Integer Independent Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Baumslag and D. Solitar, “Some two-generator one-relator non-Hopfian groups,” Bull. Am. Math. Soc 68, No. 3, 199–201 (1962).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    E. Gelman, “Subgroup growth of Baumslag–Solitar groups,” J. Group Theory 8, No. 6, 801–806 (2005).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    J. O. Button, “A formula for the normal subgroup growth of Baumslag–Solitar groups,” J. Group Theory 11, No. 6, 879–884 (2008).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    S. K. Lando, Lectures on Generating Functions [in Russian], MTsNMO, Moscow (2002); English transl.: Am. Math. Soc., Providence, RI (2003).Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations