  We have derived the X-ray luminosities of a sample of galaxies in groups,
making careful allowance for contaminating intragroup emission. The L_X:L_B and
L_X:L_{FIR} relations of spiral galaxies in groups appear to be
indistinguishable from those in other environments, however the elliptical
galaxies fall into two distinct classes. The first class is central-dominant
group galaxies which are very X-ray luminous, and may be the focus of group
cooling flows. All other early-type galaxies in groups belong to the second
class, which populates an almost constant band of L_X/L_B over the range 9.8 <
log L_B < 11.3. The X-ray emission from these galaxies can be explained by a
superposition of discrete galactic X-ray sources together with a contribution
from hot gas lost by stars, which varies a great deal from galaxy to galaxy. In
the region where the optical luminosity of the non-central group galaxies
overlaps with the dominant galaxies, the dominant galaxies are over an order of
magnitude more luminous in X-rays.
  We also compared these group galaxies with a sample of isolated early-type
galaxies, and used previously published work to derive L_X:L_B relations as a
function of environment. The non-dominant group galaxies have mean L_X/L_B
ratios very similar to that of isolated galaxies, and we see no significant
correlation between L_X/L_B and environment. We suggest that previous findings
of a steep L_X:L_B relation for early-type galaxies result largely from the
inclusion of group-dominant galaxies in samples.
