  We present B and R-band luminosity functions (LF) for a sample of 25 nearby
groups of galaxies. We find that the LFs of the groups with low X-ray
luminosity (L_X < 10^{41.7} erg/s) are significantly different from those of
the X-ray brighter groups, showing a prominent dip around M_b = -18. While both
categories show lack of late-type galaxies in their central regions, X-ray dim
groups also show a more marked concentration of optical luminosity towards the
centre. A toy simulation shows that in the low velocity dispersion environment,
as in the X-ray dim group, dynamical friction would facilitate more rapid
merging, thus depleting intermediate-luminosity galaxies to form a few giant
central galaxies, resulting in the prominent dip seen in our LFs. We suggest
that X-ray dim (or low velocity dispersion) groups are the present sites of
rapid dynamical evolution rather than their X-ray bright counterparts, and may
be the modern precursors of fossil groups. We predict that these groups of low
velocity dispersion would harbour younger stellar populations than groups or
clusters with higher velocity dispersion.
