Scales for co-compact embeddings of virtually free groups

Udo Baumgartner

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Scales for co-compact embeddings of virtually free groups

Udo Baumgartner

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Abstract

Let $Γ$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(Γ)$ be the family of totally disconnected, locally compact groups containing $Γ$ as a co-compact lattice. We prove that the values of the scale function with respect to groups in $\mathcal{F}_{td}(Γ)$ evaluated on the subset $Γ$ have only finitely many prime divisors. This can be thought of as a uniform property of the family $\mathcal{F}_{td}(Γ)$.

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Udo Baumgartner. 2006-04-10. Scales for co-compact embeddings of virtually free groups. https://arxiv.org/abs/math/0604151

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