  We study the abundance of satellite galaxies as a function of primary stellar
mass using the SDSS/DR7 spectroscopic catalogue. In contrast with previous
studies, which focussed mainly on bright primaries, our central galaxies span a
wide range of stellar mass, 10^7.5 < M_*^pri/M_sun < 10^11, from dwarfs to
central cluster galaxies. Our analysis confirms that the average number of
satellites around bright primaries, when expressed in terms of
satellite-to-primary stellar mass ratio (m_*^sat/M_*^pri), is a strong function
of M_*^pri. On the other hand, satellite abundance is largely independent of
primary mass for dwarf primaries (M_*^pri<10^10 M_sun). These results are
consistent with galaxy formation models in the LCDM scenario. We find excellent
agreement between SDSS data and semi-analytic mock galaxy catalogues
constructed from the Millennium-II Simulation. Satellite galaxies trace dark
matter substructure in LCDM, so satellite abundance reflects the dependence on
halo mass, M_200, of both substructure and galaxy stellar mass (M_*). Since
dark matter substructure is almost scale-free, the dependence of satellite
abundance on primary mass results solely from the well-defined characteristic
mass in the galaxy mass-halo mass relation. On dwarf galaxy scales, where
models predict a power-law scaling, M_* \propto M_200^2.5, similarity is
preserved and satellite abundance is independent of primary mass. For primaries
brighter than the characteristic mass of the M_*-M_200 relation, satellite
abundance increases strongly with primary mass. Our results provide strong
support for the steep, approximately power-law dependence of dwarf galaxy mass
on halo mass envisioned in LCDM galaxy formation models.
