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By comparing MgII absorption in the circumgalactic medium (CGM) of groupenvironments to isolated galaxies, we investigated the impact of environment onthe CGM. A MgII absorber is associated with a group if there are two or moregalaxies at the absorption redshift within a projected distance of D=200 kpcfrom a background quasar and a line-of-sight velocity separation of 500 km/s.We compiled a sample of 29 group environments consisting of 74 galaxies (2-5galaxies per group) at $0.113<z_{\rm gal}<0.888$. The group absorber medianequivalent width ($\langle W_r(2796)\rangle=0.65\pm0.13$ {\AA}) and coveringfraction ($f_c=0.89_{-0.09}^{+0.05}$) are larger than isolated absorbers($1.27\sigma$ and $2.2\sigma$, respectively) but median column densities arestatistically consistent. A pixel-velocity two-point correlation functionanalysis shows that group environment kinematics are statistically comparableto isolated environments ($0.8\sigma$), but with more power for high velocitydispersions similar to outflow kinematics. Group absorbers display more opticaldepth at larger velocities. A superposition model in which multiple galaxiescontribute to the observed gas matches larger equivalent width group absorbers,but overpredicts the kinematics significantly due to large velocity separationsbetween member galaxies. Finally, galaxy--galaxy groups (similar member galaxyluminosities) may have larger absorber median equivalent widths ($1.7\sigma$)and velocity dispersions ($2.5\sigma$) than galaxy--dwarf groups (disparateluminosities). We suggest the observed gas is coupled to the group rather thanindividual galaxies, forming an intragroup medium. Gas may be deposited intothis medium by multiple galaxies via outflowing winds undergoing anintergalactic transfer between member galaxies or from tidal stripping ofinteracting members.

MAGIICAT VI. The MgII Intragroup Medium is Kinematically Complex