Abstract
Let Γ be a group which is virtually free of rank at least 2 and let \({\mathcal{F}}_{td}(\Gamma)\) 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 \({\mathcal{F}}_{td}(\Gamma)\) evaluated on the subset Γ have only finitely many prime divisors. This can be thought of as a uniform property of the family \({\mathcal{F}}_{td}(\Gamma)\).
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Baumgartner, U. Scales for co-compact embeddings of virtually free groups. Geom Dedicata 130, 163–175 (2007). https://doi.org/10.1007/s10711-007-9212-2
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DOI: https://doi.org/10.1007/s10711-007-9212-2