Advertisement

Mathematische Annalen

, Volume 332, Issue 1, pp 67–79 | Cite as

Normal subgroup growth in free class-2-nilpotent groups

  • Christopher Voll
Article

Abstract.

Let F2, d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions Open image in new window prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders.

Keywords

Functional Equation Normal Subgroup Zeta Function Pole Order Subgroup Growth 
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.
    Butler, L.M.: Subgroup lattices and symmetric functions. Mem. Amer. Math. Soc. 112, (1994)Google Scholar
  2. 2.
    du Sautoy, M.P.F.: Counting p-groups and nilpotent groups. Publ. Math. I.H.E.S. 92, (2000)Google Scholar
  3. 3.
    Grunewald, F.J., du Sautoy, M.P.F.: Analytic properties of zeta functions and subgroup growth. Ann. Math. 152, 793–833 (2000)Google Scholar
  4. 4.
    Grunewald, F.J., Segal, D., Smith, G.C.: Subgroups of finite index in nilpotent groups. Invent. Math. 93, 185–223 (1988)Google Scholar
  5. 5.
    Paajanen, P.M.: The normal zeta function of F2,4. In preparationGoogle Scholar
  6. 6.
    Voll, C.: Functional equations for local normal zeta functions of nilpotent groups. Geom. Funct. Anal., with an Appendix by A. Beauville, to appear (http://arxiv.org/abs/ math.GR/0305362)

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Christopher Voll
    • 1
  1. 1.Mathematical InstituteOxfordEngland

Personalised recommendations