  The most accepted scenario for the origin of fossil groups (FGs) is that they
are galaxy associations in which the merging rate was fast and efficient. These
systems have assembled half of their mass at early epoch of the Universe,
subsequently growing by minor mergers. They could contain a fossil record of
the galaxy structure formation. We have started a project in order to
characterize a large sample of FGs. In this paper we present the analysis of
the fossil system RX J105453.3+552102. Optical deep images were used for
studying the properties of the brightest group galaxy and for computing the
photometric luminosity function of the group. We have also performed a detail
dynamical analysis of the system based on redshift data for 116 galaxies. This
galaxy system is located at z=0.47, and shows a quite large line-of-sight
velocity dispersion \sigma_{v}~1000 km/s. Assuming the dynamical equilibrium,
we estimated a virial mass of M ~ 10^{15} h_{70} M_{\odot}. No evidence of
substructure was found within 1.4 Mpc radius. We found a statistically
significant departure from Gaussianity of the group members velocities in the
most external regions of the group. This could indicate the presence of
galaxies in radial orbits in the external region of the group. We also found
that the photometrical luminosity function is bimodal, showing a lack of M_{r}
~ -19.5 galaxies. The brightest group galaxy shows low Sersic parameter (n~2)
and a small peculiar velocity. Indeed, our accurate photometry shows that the
difference between the brightest and the second brightest galaxies is 1.9 mag
in the r-band, while the classical definition of FGs is based on a magnitude
gap of 2. We conclude that this fossil system does not follow the empirical
definition of FGs. Nevertheless, it is a massive, old and undisturbed galaxy
system with little infall of L^{*} galaxies since its initial collapse.
