We study the stellar mass distribution for galaxies in 160 X-ray detected groups of 10^13<Log(M_200/M_sun)<2x10^14 and compare it with that of galaxies in the field, to investigate the action of environment on the build up of the stellar mass. We highlight differences in the build up of the passive population in the field, which imprint features in the distribution of stellar mass of passive galaxies at Log(M/M_sun)< 10.5. The gradual diminishing of the effect when moving to groups of increasing total masses indicates that the growing influence of the environment in bound structures is responsible for the build up of a quenched component at Log(M/M_sun)< 10.5. Differently, the stellar mass distribution of star forming galaxies is similar in shape in all the environments, and can be described by a single Schechter function both in groups and in the field. Little evolution is seen up to redshift 1. Nevertheless at z=0.2-0.4 groups with M_200<6x10^13 Msun (low mass groups) tend to have a characteristic mass for star forming galaxies which is 50% higher than in higher mass groups; we interpret it as a reduced action of environmental processes in such systems. Furthermore we analyse the distribution of sSFR--Log(M) in groups and in the field, and find that groups show on average a lower sSFR (by ~0.2 dex) at z<0.8. Accordingly, we find that the fraction of star forming galaxies is increasing with redshift in all environments, but at a faster pace in the denser ones. Finally our analysis highlights that low mass groups have a higher fraction (by 50%) of the stellar mass locked in star forming galaxies than higher mass systems (i.e. 2/3 of their stellar mass).
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