2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201990There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups. Applying this connection to the tri-bimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely $S_4$, the permutation group of four objects.References added. To appear in Phys. Rev. DHigh Energy Physics - Phenomenologytext