  Deviations of galaxy groups from cluster scaling relations can be understood
in terms of an excess of entropy in groups. The main effect of this excess is
to reduce the density and thus luminosity of the intragroup gas. Given this,
groups should also should show a steep relationship between X-ray luminosity
and velocity dispersion. However, previous work suggests that this is not the
case with many measuring slopes flatter than the cluster relation.
  Examining the group L_X:\sigma relation shows that much of the flattening is
caused by a small subset of groups which show very high X-ray luminosities for
their velocity dispersions (or vice versa).
  Detailed Chandra study of two such groups shows that earlier ROSAT results
were subject to significant (~30-40%) point source contamination, but confirm
that a significant hot IGM is present in these groups, although these are two
of the coolest systems in which intergalactic X-ray emission has been detected.
  Their X-ray properties are shown to be broadly consistent with those of other
galaxy groups, although the gas entropy in NGC 1587 is unusually low, and its
X-ray luminosity correspondingly high for its temperature, compared to most
groups.
  This leads us to suggest that the velocity dispersion in these systems has
been reduced in some way, and we consider how this might have come about.
