  We have performed a systematic search for X-ray cavities in the hot gas of 51
galaxy groups with Chandra archival data. The cavities are identified based on
two methods: subtracting an elliptical beta model fitted to the X-ray surface
brightness, and performing unsharp masking. 13 groups in the sample 25% are
identified as clearly containing cavities, with another 13 systems showing
tentative evidence for such structures. We find tight correlations between the
radial and tangential radii of the cavities, and between their size and
projected distance from the group center, in quantitative agreement with the
case for more massive clusters. This suggests that similar physical processes
are responsible for cavity evolution and disruption in systems covering a large
range in total mass. We see no clear association between the detection of
cavities and the current 1.4 GHz radio luminosity of the central brightest
group galaxy, but there is a clear tendency for systems with a cool core to be
more likely to harbor detectable cavities. To test the efficiency of the
adopted cavity detection procedures, we employ a set of mock images designed to
mimic typical Chandra data of our sample, and find that the model-fitting
approach is generally more reliable than unsharp masking for recovering cavity
properties. Finally, we find that the detectability of cavities is strongly
influenced by a few factors, particularly the signal-to-noise ratio of the
data, and that the real fraction of X-ray groups with prominent cavities could
be substantially larger than the 25--50% suggested by our analysis.
