  In this paper, we study the variations of group galaxy properties according
to the assembly history in SDSS-DR6 selected groups. Using mock SDSS group
catalogues, we find two suitable indicators of group formation time: i) the
isolation of the group, defined as the distance to the nearest neighbor in
terms of its virial radius, and ii) the concentration, measured as the group
inner density calculated using the fifth nearest bright galaxy to the group
centre. Groups within narrow ranges of mass in the mock catalogue show
increasing group age with isolation and concentration. However, in the
observational data the stellar age, as indicated by the spectral type, only
shows a correlation with concentration. We study groups of similar mass and
different assembly history, finding important differences in their galaxy
population. Particularly, in high mass SDSS groups, the number of members,
mass-to-light ratios, red galaxy fractions and the magnitude difference between
the brightest and second brightest group galaxies, show different trends as a
function of isolation and concentration, even when it is expected that the
latter two quantities correlate with group age. Conversely, low mass SDSS
groups appear to be less sensitive to their assembly history. The correlations
detected in the SDSS are not consistent with the trends measured in the mock
catalogues. However, discrepancies can be explained in terms of the
disagreement found in the age-isolation trends, suggesting that the model might
be overestimating the effects of environment.We discuss how the modeling of the
cold gas in satellite galaxies could be responsible for this problem. These
results can be used to improve our understanding of the evolution of galaxies
in high-density environments.
