2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111475Let $Γ$ 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)Group Theory22D05; 57M07; 20E08text