  This study is part of the FOssil Groups Origin (FOGO) project which aims at
carrying out a systematic and multiwavelength study of a large sample of fossil
systems. Here we focus on the relation between the optical luminosity (Lopt)
and X-ray luminosity (Lx). Out of a sample of 28 candidate fossil systems, we
consider a sample of 12 systems whose fossil classification has been confirmed
by a companion study. They are compared with the complementary sample of 16
systems whose fossil nature is not confirmed and with a subsample of 102 galaxy
systems from the RASS-SDSS galaxy cluster survey. Fossil and normal systems
span the same redshift range 0<z<0.5 and have the same Lx distribution. For
each fossil system, the Lx in the 0.1-2.4 keV band is computed using data from
the ROSAT All Sky Survey. For each fossil and normal system we homogeneously
compute Lopt in the r-band within the characteristic cluster radius, using data
from the SDSS DR7. We sample the Lx-Lopt relation over two orders of magnitude
in Lx. Our analysis shows that fossil systems are not statistically
distinguishable from the normal systems both through the 2D KS test and the fit
of the Lx-Lopt relation. The optical luminosity of the galaxy system does
strongly correlate with the X-ray luminosity of the hot gas component,
independently of whether the system is fossil or not. We conclude that our
results are consistent with the classical "merging scenario" of the brightest
galaxy formed via merger/cannibalism of other group galaxies, with conservation
of the optical light. We find no evidence for a peculiar state of the hot
intracluster medium.
