  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.
