  The luminosity gap between the two brightest members of galaxy groups and
clusters is thought to offer a strong test for the models of galaxy formation
and evolution. This study focuses on the statistics of the luminosity gap in
galaxy groups, in particular fossil groups, e.g. large luminosity gap, in an
analogy with the same in a cosmological simulation. We use spectroscopic legacy
data of seventh data release (DR7) of SDSS, to extract a volume limited sample
of galaxy groups utilizing modified friends-of-friends (mFoF) algorithm.
Attention is paid to galaxy groups with the brightest group galaxy (BGG) more
luminous than \Mr = -22. An initial sample of 620 groups in which 109 optical
fossil groups, where the luminosity gap exceeds 2 magnitude, were identified.
We compare the statistics of the luminosity gap in galaxy groups at low mass
range from the SDSS with the same in the Millennium simulations where galaxies
are modeled semi-analytically. We show that the BGGs residing in galaxy groups
with large luminosity gap, i.e. fossil groups, are on average brighter and live
in lower mass halos with respect to their counter parts in non-fossil systems.
Although low mass galaxy groups are thought to have recently formed, we show
that in galaxy groups with 15 galaxies brighter than $M_r\ge -19.5$,
evolutionary process are most likely to be responsible for the large luminosity
gap. We also examine a new probe of finding fossil group. In addition we extend
the recently introduced observational probe based on the luminosity gap, the
butterfly diagram, to galaxy groups and study the probe as a function of halo
mass. This probe can, in conjunction with the luminosity function, help to fine
tune the semi-analytic models of galaxies employed in the cosmological
simulations.
