Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system

In this paper, we investigate the effects of spontaneously generated coherence (SGC) on the conditions for exhibiting lasing without inversion (LWI) in the presence of a weak probe and a strong-coupling field. We find that owing to the effect of SGC, LWI can be realized without the incoherent pumping or the decay between two upper levels. However, in the region where LWI can be exhibited, the effect of SGC term on the exhibition of LWI is not always positive, sometimes it can even cumber the realization of LWI for some values of SGC. These values are given in this paper. In addition, we also analyze the essence of the generation of the probe field.