  Combining our knowledge of halo structure and internal kinematics from
cosmological dark matter simulations and the distribution of halo interlopers
in projected phase space measured in cosmological galaxy simulations, we
develop MAGGIE, a prior- and halo-based, probabilistic, abundance matching (AM)
grouping algorithm for doubly complete subsamples (in distance and luminosity)
of flux-limited samples. We test MAGGIE-L and MAGGIE-M (in which group masses
are derived from AM applied to the group luminosities and stellar masses,
respectively) on groups of at least three galaxies extracted from a mock Sloan
Digital Sky Survey Legacy redshift survey, incorporating realistic
observational errors on galaxy luminosities and stellar masses. In comparison
with the optimal Friends-of-Friends (FoF) group finder, groups extracted with
MAGGIE are much less likely to be secondary fragments of true groups; in
primary fragments, its galaxy memberships (relative to the virial sphere of the
real-space group) are much more complete and usually more reliable, and its
masses are much less biased and usually with less scatter, as are its group
luminosities and stellar masses (computed in MAGGIE using the membership
probabilities as weights). FoF outperforms MAGGIE only for high-mass clusters:
for the reliability of the galaxy population and the dispersion of its total
mass. In comparison with our implementation of the Yang et al. group finder,
MAGGIE reaches much higher completeness and slightly lower group fragmentation
and dispersion on group total masses, luminosities and stellar masses, but
slightly greater bias in the latter two and lower reliabilities. MAGGIE should
therefore lead to sharper trends of environmental effects on galaxies and more
accurate mass/orbit modelling.
