Title

The asymptotic density of finite-order elements in virtually nilpotent groups

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

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