  We study the evolution of galaxies inside and outside of the group
environment since z=1 using a large well defined set of groups and galaxies
from the zCOSMOS-bright redshift survey in the COSMOS field. The fraction of
galaxies with early-type morphologies increases monotonically with M_B
luminosity and stellar mass and with cosmic epoch. It is higher in the groups
than elsewhere, especially at later epochs. The emerging environmental effect
is superposed on a strong global mass-driven evolution, and at z~0.5 and
log(M*/Msol)~10.2, the "effect" of group environment is equivalent to (only)
about 0.2 dex in stellar mass or 2 Gyr in time. The stellar mass function of
galaxies in groups is enriched in massive galaxies. We directly determine the
transformation rates from late to early morphologies, and for transformations
involving colour and star formation indicators. The transformation rates are
systematically about twice as high in the groups as outside, or up to 3-4 times
higher correcting for infall and the appearance of new groups. The rates reach
values, for masses around the crossing mass 10^10.5 Msol, as high as
(0.3-0.7)/Gyr in the groups, implying transformation timescales of 1.4-3 Gyr,
compared with less than 0.2/Gyr, i.e. timescales >5 Gyr, outside of groups. All
three transformation rates decrease at higher stellar masses, and must decrease
also at the lower masses below 10^10 Msol which we cannot well probe. The rates
involving colour and star formation are consistently higher than those for
morphology, by a factor of about 50%. Our conclusion is that the
transformations which drive the evolution of the overall galaxy population
since z~1 must occur at a rate 2-4 times higher in groups than outside of them.
