2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135210A pseudomodular group is a finite coarea nonarithmetic Fuchsian group whose cusp set is exactly $\mathbb{P}^1(\mathbb{Q})$. Long and Reid constructed finitely many of these by considering Fricke groups, i.e., those that uniformize one-cusped tori. We prove that a zonal Fricke group with rational cusps is pseudomodular if and only if its cusp set is dense in the finite adeles of $\mathbb{Q}$. We then deduce that infinitely many such Fricke groups are not pseudomodular.4 pagesNumber Theory20H10text