We present results of two 21-cm H i surveys performed with the Australia Telescope Compact Array in the nearby Centaurus A and Sculptor galaxy groups .
These surveys are sensitive to compact H i clouds and galaxies with H i masses as low as \sim 3 \times 10 ^ { 6 } M _ { \odot } , and are therefore among the most sensitive extragalactic H i 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 H i 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 } M _ { \odot } in these groups , we would have expected \sim 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 H i surveys that a H i rich population of these satellites does not exist .