Let Γ be a finitely generated group with a given word metric. The asymptotic density of elements in Γ that have a particular property P is the limit, as r → ∞, 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). © 2007 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Journal of Algebra
Dani, P. (2007). The asymptotic density of finite-order elements in virtually nilpotent groups. Journal of Algebra, 316 (1), 54-78. https://doi.org/10.1016/j.jalgebra.2007.06.023