  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).
