  Semi-analytic models (SAMs) are currently one of the primary tools with which
to model statistically significant ensembles of galaxies. The underlying
physical prescriptions inherent to each SAM are, in many cases, different from
one another. Several SAMs have been applied to the dark matter merger trees
extracted from the Millennium Run, including those associated with the
well-known Munich and Durham lineages. We compare the predicted luminosity
distributions of galaxy groups using four publicly available SAMs (De Lucia et
al. 2006; Bower et al. 2006; Bertone et al. 2007; Font et al. 2008), in order
to explore a galactic environment in which the models have not been explored to
the same degree as they have in the field or in rich clusters. We identify a
characteristic "wiggle" in the group galaxy luminosity function generated using
the De Lucia et al. (2006) SAM, that is not present in the Durham-based models,
consistent to some degree with observations. However, a comparison between
conditional luminosity functions of groups between the models and observations
of Yang et al. (2007) suggest that neither model is a particularly good match.
The luminosity function wiggle is interpreted as the result of the two-mode AGN
feedback implementation used in the Munich models, which itself results in
flattened magnitude gap distribution. An associated analysis of the magnitude
gap distribution between first- and second-ranked group galaxies shows that
while the Durham models yield distributions with approximately equal luminosity
first- and second-ranked galaxies, in agreement with observations, the De Lucia
et al. models favours the scenario in which the second-ranked galaxy is
approximately one magnitude fainter than the primary,especially when the
dynamic range of the mock data is limited to 3 magnitudes.
