Scales for co-compact embeddings of virtually free groups

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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 $\mathcal{F}_{td}(Γ)$.
12 pages; key words: uniform lattice, virtually free group, totally disconnected group, scale function (Error in references corrected in version 2)

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Group Theory, 22D05; 57M07; 20E08

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http://salesiana.dossiersoluciones.com/handle/123456789/111475

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604151
 http://arxiv.org/abs/math/0604151

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arXiv