Skip to main content
Log in

On the degree of polynomial subgroup growth in class 2 nilpotent groups

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We use the theory of zeta functions of groups to establish a lower limit for the degree of polynomial normal subgroup growth in class two nilpotent groups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. P. F. du Sautoy, A nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups, Israel Journal of Mathematics 126 (2001), 269–288.

    MATH  MathSciNet  Google Scholar 

  2. M. P. F. du Sautoy and F. J. Grunewald, Analytic properties of zeta functions and subgroup growth, Annals of Mathematics 152 (2000), 793–833.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. J. Grunewald, D. Segal and G. C. Smith, Subgroups of finite index in nilpotent groups, Inventiones Mathematicae 93 (1988), 185–223.

    Article  MATH  MathSciNet  Google Scholar 

  4. B. Klopsch, Linear bounds for the degree of subgroup growth in terms of the Hirsch length, The Bulletin of the London Mathematical Society 32 (2000), 403–408.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. M. Paajanen, The local normal zeta function of the class two free nilpotent group on four generators, Geometriae Dedicata 115 (2005), 135–162.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. M. Paajanen, Zeta functions of groups and arithmetic geometry, D.Phil. thesis, Oxford, 2005.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paajanen, P.M. On the degree of polynomial subgroup growth in class 2 nilpotent groups. Isr. J. Math. 157, 323–332 (2007). https://doi.org/10.1007/s11856-006-0014-2

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-006-0014-2

Keywords

Navigation