Because of the redshift-dependent mass completeness limits for the star-forming and quiescent galaxies, the star-forming and all galaxy samples at low-$z$ are probed in four and three bins, respectively, while at high-$z$, there are only three bins for the star-forming galaxies and two bins for all galaxies.

To quantitatively describe our results, the SSFRs of star-forming galaxies are fit with a linear relation log$_{10}$(SSFR/yr$^{-1}$) = $\alpha$ $\times$ ($r_p$/Mpc) + $\beta$ for $r_p$ $<$ 2.0 [Mpc]{} and the best-fit parameters are listed in Table \[tab:ssfrfitting\]. At fixed mass, the SSFR deficit of group to field galaxies is $<$ 0.1 dex, consistent with our previous finding in [@lin14]. That is, the median SSFRs of star-forming galaxies in the group environment in both redshift bins are roughly independent of the $r_p$, suggesting that the environmental quenching effect is likely dominated by a fast mechanism. However, we note that the 0.1 dex reduction of the SSFR for low-mass group galaxies has a 2.5$\sigma$ confidence and is small, but not totally negligible. On the other hand, in the cluster environment, the SSFRs of the star-forming galaxies show strong scatter between the center and field, with a difference $<$ $\sim$ 0.2 dex in less massive galaxy 