  The Connes and Lott reformulation of the strong and electroweak model
represents a promising application of noncommutative geometry. In this scheme
the Higgs field naturally appears in the theory as a particular `gauge boson',
connected to the discrete internal space, and its quartic potential, fixed by
the model, is not vanishing only when more than one fermion generation is
present. Moreover, the exact hypercharge assignments and relations among the
masses of particles have been obtained. This paper analyzes the possibility of
extensions of this model to larger unified gauge groups. Noncommutative
geometry imposes very stringent constraints on the possible theories, and
remarkably, the analysis seems to suggest that no larger gauge groups are
compatible with the noncommutative structure, unless one enlarges the fermionic
degrees of freedom, namely the number of particles.
