  We probe the diffuse stellar mass in a sample of 1401 low redshift galaxy
groups (10E13 - 10E14 Msun/h) by examining the rate of hostless Type Ia
supernova (SNe Ia) within the groups. We correlate the sample of confirmed SNe
Ia from the SDSS supernova survey with the positions of our galaxy groups, as
well as with the resolved galaxies within them. We find that 19 of the 59 SNe
Ia within the group sample have no detectable host galaxy, with another three
ambiguous instances. This gives a robust upper limit that a maximum of 2.69%
+1.58%/-1.34% of the group's total mass arises from diffuse stars in the
intragroup medium. After correcting for a contribution from "prompt" SNe
occurring within galaxies, and including a contribution from those which arise
in dwarf galaxies below our photometric limit, we find that only 1.32%
+0.78%/-0.70% of the group's total mass is likely in the form of diffuse
stellar mass. Combining this result with the galaxy stellar mass functions of
Yang et al., we find that 47% +16%/-15% of the stellar mass in our groups is in
the form of diffuse light, so that stars make up a fraction 0.028 +0.011/-0.010
of the total group mass. Galaxy groups appear to be very efficient in
disrupting stellar mass into a diffuse component; however, stars still make up
a small fraction of the group mass, comparable to that seen in rich clusters.
This remains a challenge to galaxy formation models.
