  The gap between first and second ranked galaxy magnitudes in groups is often
considered a tracer of their merger histories, which in turn may affect galaxy
properties, and also serves to test galaxy luminosity functions (LFs). We
remeasure the conditional luminosity function (CLF) of the Main Galaxy Sample
of the SDSS in an appropriately cleaned subsample of groups from the Yang
catalog. We find that, at low group masses, our best-fit CLF have steeper
satellite high ends, yet higher ratios of characteristic satellite to central
luminosities in comparison with the CLF of Yang et al. (2008). The observed
fractions of groups with large and small magnitude gaps as well as the Tremaine
& Richstone (1977) statistics, are not compatible with either a single
Schechter LF or with a Schechter-like satellite plus lognormal central LF.
These gap statistics, which naturally depend on the size of the subsamples, and
also on the maximum projected radius, $R_{\rm max}$, for defining the 2nd
brightest galaxy, can only be reproduced with two-component CLFs if we allow
small gap groups to preferentially have two central galaxies, as expected when
groups merge. Finally, we find that the trend of higher gap for higher group
velocity dispersion, $\sigma_{\rm v}$, at given richness, discovered by Hearin
et al. (2013), is strongly reduced when we consider $\sigma_{\rm v}$ in bins of
richness, and virtually disappears when we use group mass instead of
$\sigma_{\rm v}$. This limits the applicability of gaps in refining
cosmographic studies based on cluster counts.

Astrophysics of Galaxies