  We study the change of the probe field group velocity from subluminal to
superluminal range for two kinds of closed three-level V-type system with
spontaneously generated coherence and incoherent pumping field. For the first
kind of the V-type system we deduce the analytical formula of the group
velocity, while for the second kind of the V-type system we solve numerically
the density matrix equations system and apply it to a real system from the LiH
molecule. We find that the group index of the probe field can be changed from
positive to negative within the appropriate choice of the relative phase
between the probe and coupling field phases, the incoherent pumping rate and
probe detuning.
