Document Type
Article
Publication Date
10-1-2007
Abstract
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
First Page
54
Last Page
78
Recommended Citation
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