Context. Studying theevolution of galaxies located within groups may have important implications for our understanding of the global evolution of the galaxy population as a whole. The fraction of galaxies bound in groups at z ~ 0 is as high as 60% and therefore any mechanism (among the many suggested) that could quench star formation when a galaxy enters group environment would be an important driver for galaxy evolution. Aims: Using the group catalog obtained from zCOSMOS spectroscopic data and the complementary photometric data from the COSMOS survey, we explore segregation effects occurring in groups of galaxies at intermediate/high redshifts. Our aim is to reveal if, and how significantly, group environment affects the evolution of infalling galaxies. Methods: We built two composite groups at intermediate (0.2 ≤ z ≤ 0.45) and high (0.45 < z ≤ 0.8) redshifts, and we divided the corresponding composite group galaxies into three samples according to their distance from the group center. The samples roughly correspond to galaxies located in a group's inner core, intermediate, and infall region. We explored how galaxy stellar masses and colors - working in narrow bins of stellar masses - vary as a function of the galaxy distance from the group center. Results: We found that the most massive galaxies in our sample (log (ℳgal/ℳ&sun;) ≥ 10.6) do not display any strong group-centric dependence of the fractions of red/blue objects. For galaxies of lower masses (9.8 ≤ log (ℳgal/ℳ&sun;) ≤ 10.6) there is a radial dependence in the changing mix of red and blue galaxies. This dependence is most evident in poor groups, whereas richer groups do not display any obvious trend of the blue fraction. Interestingly, mass segregation shows the opposite behavior: it is visible only in rich groups, while poorer groups have a a constant mix of galaxy stellar masses as a function of radius. Conclusions: These findings can be explained in a simple scenario where color- and mass-segregation originate from different physical processes. While dynamical friction is the obvious cause for establishing mass segregation, both starvation and galaxy-galaxy collisions are plausible mechanisms to quench star formation in groups at a faster rate than in the field. In poorer groups the environmental effects are caught in action superimposed to secular galaxy evolution. Their member galaxies display increasing blue fractions when moving from the group center to more external regions, presumably reflecting the recent accretion history of these groups. Based on observations made at the European Southern Observatory (ESO) Very Large Telescope (VLT) under Large Program 175.A-0839.