  We study the evolution of the red galaxy fraction (f_red) in 905 galaxy
groups with 0.15 < z < 0.52. The galaxy groups are identified by the
`probability Friends-of-Friends' algorithm from the first Red-Sequence Cluster
Survey (RCS1) photometric-redshift sample. There is a high degree of uniformity
in the properties of the red-sequence of the group galaxies, indicating that
the luminous red-sequence galaxies in the groups are already in place by z~0.5
and that they have a formation epoch of z>2. In general, groups at lower
redshifts exhibit larger f_red than those at higher redshifts, showing a group
Butcher-Oemler effect. We investigate the evolution of f_red by examining its
dependence on four parameters, which can be classified as one intrinsic and
three environmental: galaxy stellar mass (M_*), total group stellar
mass(M_{*,grp}, a proxy for group halo mass), normalized group-centric radius
(r_grp), and local galaxy density (Sigma_5). We find that M_* is the dominant
parameter such that there is a strong correlation between f_red and galaxy
stellar mass. Furthermore, the dependence of f_red on the environmental
parameters is also a strong function of M_*. Massive galaxies (M_* > 10^11
M_sun) show little dependence of f_red on r_grp, M_{*,grp}, and Sigma_5 over
the redshift range. The dependence of f_red on these parameters is primarily
seen for galaxies with lower masses, especially for M_* < 10^{10.6} M_{sun}. We
observe an apparent `group down-sizing' effect, in that galaxies in lower-mass
halos, after controlling for galaxy stellar mass, have lower f_red. We find a
dependence of \fred on both \rgrp and \SigmaF after the other parameters are
controlled. At a fixed \rgrp, there is a significant dependence of f_red on
Sigma_5, while r_grp gradients of f_red are seen for galaxies in similar
Sigma_5 regions. This indicates .....
