  There is a correlation between bulge mass of the three main galaxies of the
Local Group (LG), i.e. M31, Milky Way (MW), and M33, and the number of their
dwarf spheroidal galaxies. A similar correlation has also been reported for
spiral galaxies with comparable luminosities outside the LG. These correlations
do not appear to be expected in standard hierarchical galaxy formation. In this
contribution, and for the first time, we present a quantitative investigation
of the expectations of the standard model of cosmology for this possible
relation using a galaxy catalogue based on the Millennium-II simulation. Our
main sample consists of disk galaxies at the centers of halos with a range of
virial masses similar to M33, MW, and M31. For this sample, we find an average
trend (though with very large scatter) similar to the one observed in the LG;
disk galaxies in heavier halos on average host heavier bulges and larger number
of satellites. In addition, we study sub-samples of disk galaxies with very
similar stellar or halo masses (but spanning a range of 2-3 orders of magnitude
in bulge mass) and find no obvious trend in the number of satellites vs. bulge
mass. We conclude that while for a wide galaxy mass range a relation arises
(which seems to be a manifestation of the satellite number - halo mass
correlation), for a narrow one there is no relation between number of
satellites and bulge mass in the standard model. Further studies are needed to
better understand the expectations of the standard model for this possible
relation.
