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Galaxy Group at z=0.3 Associated with the Damped Lyman Alpha System Towards Quasar Q1127-145

(Abridged) We performed a spectroscopic galaxy survey, complete to m<20.3 (L_B>0.15L_B* at z=0.3), within 100x100" of the quasar Q1127-145 (z=1.18). The VLT/UVES quasar spectrum contains three z<0.33 MgII absorption systems. We obtained eight new galaxy redshifts, adding to the four previously known, and galaxy star formation rates and metallicities were computed where possible. A strong MgII system [W_r(2796)=1.8A], which is a known DLA, had three previously identified galaxies; we found two additional galaxies associated with this system. These five galaxies form a group with diverse properties, such as a luminosity range of 0.04<L_B<0.63L_B*, an impact parameter range of 17<D<241kpc and velocity dispersion of 115km/s. The DLA group galaxy redshifts span beyond the 350km/s velocity spread of the metallic absorption lines of the DLA itself. The two brightest group galaxies have SFRs of a few Msun/yr and should not have strong winds. We have sufficient spectroscopic information to directly compare three of the five group galaxies' (emission-line) metallicities with the DLA (absorption) metallicity: the DLA metallicity is 1/10th solar, substantially lower than the three galaxies' which range between less than 1/2 solar to solar metallicity. HST/WFPC-2 imaging shows perturbed morphologies for the three brightest group galaxies, with tidal tails extending 25kpc. We favor a scenario where the DLA absorption originates from tidal debris in the group environment. Another absorber exhibits weak MgII absorption [W_r(2796)=0.03A] and had a previously identified galaxy at a similar redshift. We have identified a second galaxy associated with this system. Both galaxies have solar metallicities and unperturbed morphologies. The SFR of one galaxy is much lower than expected for strong outflows. Finally, we have identified five galaxies at large impact parameters with no associated MgII absorption.