  We analyse the dependence of the luminosity function of galaxies in groups
(LF) on group dynamical state. We use the Gaussianity of the velocity
distribution of galaxy members as a measurement of the dynamical equilibrium of
groups identified in the SDSS Data Release 7 by Zandivarez & Martinez. We apply
the Anderson-Darling goodness-of-fit test to distinguish between groups
according to whether they have Gaussian or Non-Gaussian velocity distributions,
i.e., whether they are relaxed or not. For these two subsamples, we compute the
$^{0.1}r-$band LF as a function of group virial mass and group total
luminosity. For massive groups, ${\mathcal M}>5 \times 10^{13} \ M_{\odot} \
h^{-1}$, we find statistically significant differences between the LF of the
two subsamples: the LF of groups that have Gaussian velocity distributions have
a brighter characteristic absolute magnitude ($\sim0.3$ mag) and a steeper
faint end slope ($\sim0.25$). We detect a similar effect when comparing the LF
of bright ($M^{group}_{^{0.1}r}-5\log(h)<-23.5$) Gaussian and Non-Gaussian
groups. Our results indicate that, for massive/luminous groups, the dynamical
state of the system is directly related with the luminosity of its galaxy
members.
