Super-exponential distortion of subgroups of CAT(-1) groups
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.
math.GR↗
arXiv subjects
Pallavi Dani
Publications and source records attributed to Pallavi Dani.
The asymptotic density of finite-order elements in virtually nilpotent groups
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).
math.GR↗