  We use Chandra observations of 13 nearby groups of galaxies to investigate
the hot gas content of their member galaxies. We find that a large fraction of
near-IR bright, early-type galaxies in groups have extended X-ray emission,
indicating that they retain significant hot gas halos even in these dense
environments. In particular, we detect hot gas halos in ~80% of L_K > L_star
galaxies. We do not find a significant difference in the L_K-L_X relation for
detected group and cluster early-type galaxies. However, we detect X-ray
emission from a significantly higher fraction of galaxies brighter than L_star
in groups compared to clusters, indicating that a larger fraction of galaxies
in clusters experience significant stripping of their hot gas. In addition,
group and cluster galaxies appear to be X-ray faint compared to field galaxies,
though a Chandra based field sample is needed to confirm this result. The
near-IR bright late-types galaxies in clusters and groups appear to follow the
L_K-L_X relation for early-type galaxies, while near-IR fainter late-type
galaxies are significantly more X-ray luminous than this relation likely due to
star formation. Finally, we find individual examples of ongoing gas stripping
of group galaxies. One galaxy shows a 40-50 kpc X-ray tail, and two merging
galaxy systems show tidal bridges/tails of X-ray emission. Therefore, stripping
of hot galactic gas through both ram pressure and tidal forces does occur in
groups and clusters, but the frequency or efficiency of such events must be
moderate enough to allow hot gas halos in a large fraction of bright galaxies
to survive even in group and cluster cores.
