2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190544We analize the different ways for the spontaneous breaking of the gauge symmetry, for the $[SU(6)]^3\otimes Z_3$ family unification model. In particular we study the consequences of a previous selection for the vacuum expectation values of the Higgs fields, showing that such set predicts unwanted flavor changing neutral currents at the $m_Z=91 GeVs$ mass scale. A new set of vacuum expectation values which solves this problem is proposed.19 pages, Latex file, No figures. To appear in Rev. Mex. FisHigh Energy Physics - Phenomenologytext