  We describe a general method to study the ground state phase diagram of
electronic models on chains whose extended Hubbard hamiltonian is formed by a
generalized permutator plus a band-controlling term. The method, based on the
appropriate interpretation of Sutherland's species, yields under described
conditions a reduction of the effective Hilbert space. In particular, we derive
the phase diagrams of two new models; the first one exhibits a band-controlled
insulator-superconductor transition at half-filling for the unusually high
value $U_c=6 t$; the second one is characterized by a filling-controlled
metal-insulator transition between two finite regions of the diagram.
