  We present the results of a search for extended X-ray sources and their
corresponding galaxy groups from 800-ks Chandra coverage of the All-wavelength
Extended Groth Strip International Survey (AEGIS). This yields one of the
largest X-ray selected galaxy group catalogs from a blind survey to date. The
red-sequence technique and spectroscopic redshifts allow us to identify 100$%$
of reliable sources, leading to a catalog of 52 galaxy groups. The groups span
the redshift range $z\sim0.066-1.544$ and virial mass range
$M_{200}\sim1.34\times 10^{13}-1.33\times 10^{14}M_\odot$. For the 49 extended
sources which lie within DEEP2 and DEEP3 Galaxy Redshift Survey coverage, we
identify spectroscopic counterparts and determine velocity dispersions. We
select member galaxies by applying different cuts along the line of sight or in
projected spatial coordinates. A constant cut along the line of sight can cause
a large scatter in scaling relations in low-mass or high-mass systems depending
on the size of cut. A velocity dispersion based virial radius can more
overestimate velocity dispersion in comparison to X-ray based virial radius for
low mass systems. There is no significant difference between these two radial
cuts for more massive systems. Independent of radial cut, overestimation of
velocity dispersion can be created in case of existence of significant
substructure and also compactness in X-ray emission which mostly occur in low
mass systems. We also present a comparison between X-ray galaxy groups and
optical galaxy groups detected using the Voronoi-Delaunay method (VDM) for
DEEP2 data in this field.
