We describe X-ray observations with Chandra and XMM-Newton of 18 galaxy groups (M_group ~ 1-6x10^13 Msolar, z~0.05) from the Zurich Environmental Study (ZENS). We aim to establish the frequency and properties, unaffected by host galaxy dilution and obscuration, of AGNs in central and satellite galaxy members, also as a function of halo-centric distance. X-ray point-source detections are reported for 22 of 177 observed galaxies, down to a limit of f_(0.5-8 keV) ~ 5x10^-15 erg cm^-2 s^-1, corresponding to a limiting luminosity of L_(0.5-8 keV)~3x10^40 erg s^-1. With the majority of the X-ray sources attributed to AGNs of low-to-moderate levels (L/L_Edd>~10^-4), we discuss the detection rate in the context of the occupation of AGNs to halos of this mass scale and redshift, and compare the structural/morphological properties between AGN-active and non-active galaxies of different rank and location within the group halos. We see a slight tendency for AGN hosts to have either relatively brighter/denser disks (or relatively fainter/diffuse bulges) than non-active galaxies of similar mass. At galaxy mass scales <10^11 Msolar, central galaxies appear to be a factor ~4 more likely to host AGNs than satellite galaxies of similar mass. This effect, coupled with the tendency for AGNs to reside in massive galaxies, explains the (weak) trend for AGNs to be preferentially found in the inner regions of groups, with no detectable trend with halo-centric distance in the frequency of AGNs within the satellite population. Finally, our data support other analyses in finding that the rate of decline with redshift of AGN activity in groups matches that of the global AGN population, indicating that either AGNs occur preferentially in groups, or that the evolution rate is independent of halo mass. These trends are of potential importance, and require X-ray coverage of a larger sample to be solidly confirmed.
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