The asymptotic density of finite-order elements in virtually nilpotent groups
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
Let G be a finitely generated group with a given word metric. The asymptotic density of elements in G that have a particular property P is defined to be the limit, as r goes to infinity, of the proportion of elements in the ball of radius r which have the property P. We obtain a formula to compute the asymptotic density of finite-order elements in any virtually nilpotent group. Further, we show that the spectrum of numbers that occur as such asymptotic densities consists of exactly the rational numbers in [0,1).
Cite
@article{arxiv.math/0601126,
title = {The asymptotic density of finite-order elements in virtually nilpotent groups},
author = {Pallavi Dani},
journal= {arXiv preprint arXiv:math/0601126},
year = {2007}
}
Comments
26 pages