  We show that the one-dimensional extended Hubbard model has saturated
ferromagnetic ground states with the spin-triplet electron pair condensation in
a certain range of parameters. The ground state wave functions with fixed
electron numbers are explicitly obtained. We also construct two ground states
in which both the spin-rotation and the gauge symmetries are broken, and show
that these states are transferred from one to the other by applying the edge
operators. The edge operators are reduced to the Majorana fermions in a special
case. These symmetry breaking ground states are shown to be stabilized by a
superconducting mean field Hamiltonian which is related to the Kitaev chain
with the charge-charge interaction.
