  We present results of two 21-cm HI surveys performed with the Australia
Telescope Compact Array in the nearby Centaurus A and Sculptor galaxy groups.
These surveys are sensitive to compact HI clouds and galaxies with HI masses as
low as 3E+06 Msun, and are therefore among the most sensitive extragalactic HI
surveys to date. The surveys consist of sparsely spaced pointings that sample
approximately 2% of the groups' area on the sky. We detected previously known
group members, but we found no new HI clouds or galaxies down to the
sensitivity limit of the surveys. If the HI mass function had a faint end slope
of alpha = 1.5 below M_{HI} = 10^{7.5} Msun in these groups, we would have
expected ~3 new objects. Cold dark matter theories of galaxy formation predict
the existence of a large number low mass DM sub-halos that might appear as tiny
satellites in galaxy groups. Our results support and extend similar conclusions
derived from previous HI surveys that a HI rich population of these satellites
does not exist.
