Zeta functions of virtually nilpotent groups

@article{Sulca2012ZetaFO,
  title={Zeta functions of virtually nilpotent groups},
  author={Diego Sulca},
  journal={Israel Journal of Mathematics},
  year={2012},
  volume={213},
  pages={371-398}
}
  • Diego Sulca
  • Published 20 May 2012
  • Mathematics
  • Israel Journal of Mathematics
We prove that the subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group are finite sums of Euler products of cone integrals over Q and we deduce from this that they have rational abscissa of convergence and some meromorphic continuation. We also define Mal’cev completions of a finitely generated virtually nilpotent group and we prove that the subgroup growth and the normal subgroup growth of the latter are invariants of its Q-Mal’cev completion. 
3 Citations
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Nilpotent Groups
TLDR
The concept of the nilpotent group is described and some properties of thenilpotent groups are described.
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