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Based on a large sample of 254 220 galaxies in 81 089 groups, which areselected from the spectroscopic galaxy sample of the SDSS DR12, we investigatethe radial distribution of incidences, morphologies, environmental densities,and star formation properties of the active galactic nucleus (AGN) hostgalaxies and star-forming galaxies (SFGs) in the groups at z<0.2, as well astheir changes with group richness ($N_{\rm rich}$). It is found that AGNfraction slightly declines with richness for the groups/clusters. The SFGfraction is on average about 2 times larger than the AGN fraction, with asignificant declining trend with richness. The group AGNs are preferentiallyreside in spheroidal and bulge-dominated disc galaxies, whereas the majority ofSFGs are late-type discs. Compared with the SFGs, the AGNs in poor groups ($5\leqslant N_{\rm rich} \leqslant 10$) are closer to group center. The AGNfraction does not change with the distance to the group center, whereas the SFGfraction tends to be higher in the outskirts. The AGNs in groups have a higherincidence than the SFGs for the massive ($\log(M_*/M_{\odot}) > 10.7$)galaxies, and the mean SFG fraction is about 6 times as that of AGNs in thelate-type galaxies with lower masses at larger radius. The distribution ofenvironmental luminosity densities shows that the AGNs are likely to be residein a denser environment relative to the SFGs. Compared with the SFGs in groups,the group AGNs are found to have a higher mean stellar mass, a lower mean starformation rate, and an older mean stellar age.

Effect of richness on AGN and star formation activities in SDSS galaxy groups