  The conditions for the fragmentation of the baryonic component during merging
of dark matter halos in the early Universe are studied. We assume that the
baryonic component undergoes a shock compression. The characteristic masses of
protostellar molecular clouds and the minimum masses of protostars formed in
these clouds decrease with increasing halo mass. This may indicate that the
initial stellar mass function in more massive galaxies was shifted towards
lower masses during the initial stages of their formation. This would result in
an increase of the number of stars per unit halo mass, i.e., the efficiency of
star formation.
