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| - Constraints on the space density of low mass galaxies
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| - An $\ion{H}{i}$ survey of the Centaurus and Sculptor groups
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| - We present results of two 21-cm $\ion{H}{i}$ surveys performed with the Australia Telescope Compact Array in the nearby Centaurus A and Sculptor galaxy groups. These surveys are sensitive to compact $\ion{H}{i}$ clouds and galaxies with $\ion{H}{i}$ masses as low as ~ $ 3 \times 10^6\ M_{odot}$, and are therefore among the most sensitive extragalactic $\ion{H}{i}$ 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 $\ion{H}{i}$ clouds or galaxies down to the sensitivity limit of the surveys. If the $\ion{H}{i}$ mass function had a faint end slope of $\alpha = 1.5$ below $M_{\ion{H}{i}} = 10^{7.5}~ M_{odot}$ 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 dark matter sub-halos that might appear as tiny satellites in galaxy groups. Our results support and extend similar conclusions derived from previous $\ion{H}{i}$ surveys that a $\ion{H}{i}$ rich population of these satellites does not exist.
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