  We present a study on the variations of the luminosity function of galaxies
around clusters in a numerical simulation with semi-analytic galaxies,
attempting to detect these variations in the 2dF Galaxy Redshift Survey. We
subdivide the simulation box in equal-density regions around clusters, which we
assume can be achieved by selecting objects at a given normalised distance
($r/r_{rms}$, where $r_{rms}$ is an estimate of the halo radius) from the group
centre. The semi-analytic model predicts important variations in the luminosity
function out to $r/r_{rms}\simeq5$. In brief, variations in the mass function
of haloes around clusters (large dark-matter haloes with
$M>10^{12}$h$^{-1}$M$_{\sun}$) lead to cluster central regions that present a
high abundance of bright galaxies (high $M^*$ values) as well as low luminosity
galaxies (high $\alpha$); at $r/r_{rms}\simeq 3$ there is a lack of bright
galaxies, which shows the depletion of galaxies in the regions surrounding
clusters (minimum in $M^*$ and $\alpha$), and a tendency to constant luminosity
function parameters at larger cluster-centric distances. We take into account
the observational biases present in the real data by reproducing the peculiar
velocity effect on the redshifts of galaxies in the simulation box, and also by
producing mock catalogues. We find that excluding from the analysis galaxies
wich in projection are close to the centres of the groups provides results that
are qualitatively consistent with the full simulation box results.
