  We present the discovery of seven X-ray emitting groups of galaxies selected
as extended X-ray sources in the 200 ksec Chandra coverage of the
All-wavelength Extended Groth Strip International Survey (AEGIS). In addition,
we report on AGN activity associated to these systems. Using the DEEP2 Galaxy
Redshift Survey coverage, we identify optical counterparts and determine
velocity dispersions. In particular, we find three massive high-redshift groups
at z>0.7, one of which is at z=1.13, the first X-ray detections of
spectroscopically selected DEEP2 groups. We also present a first look at the
the L_X-T, L_X-sigma, and sigma-T scaling relations for high-redshift massive
groups. We find that the properties of these X-ray selected systems agree well
with the scaling relations of similar systems at low redshift, although there
are X-ray undetected groups in the DEEP2 catalogue with similar velocity
dispersions. The other three X-ray groups with identified redshifts are
associated with lower mass groups at z~0.07 and together form part of a large
structure or "supergroup" in the southern portion of the AEGIS field. All of
the low-redshift systems are centred on massive elliptical galaxies, and all of
the high-redshift groups have likely central galaxies or galaxy pairs. All of
the central group galaxies host X-ray point sources, radio sources, and/or show
optical AGN emission. Particularly interesting examples of central AGN activity
include a bent-double radio source plus X-ray point source at the center of a
group at z=0.74, extended radio and double X-ray point sources associated to
the central galaxy in the lowest-redshift group at z=0.066, and a bright green
valley galaxy (part of a pair) in the z=1.13 group which shows optical AGN
emission lines.
