  We re-examine the fraction of low-redshift Sloan Digital Sky Survey
satellites and centrals in which star formation has been quenched, using the
environment quenching efficiency formalism that separates out the dependence of
stellar mass. We show that the centrals of the groups containing the satellites
are responding to the environment in the same way as their satellites (at least
for stellar masses above 10^10.3 Msun), and that the well-known differences
between satellites and the general set of centrals arise because the latter are
overwhelmingly dominated by isolated galaxies. The widespread concept of
"satellite quenching" as the cause of environmental effects in the galaxy
population can therefore be generalized to "group quenching". We then explore
the dependence of the quenching efficiency of satellites on overdensity,
group-centric distance, halo mass, the stellar mass of the satellite, and the
stellar mass and specific star formation rate (sSFR) of its central, trying to
isolate the effect of these often interdependent variables. We emphasize the
importance of the central sSFR in the quenching efficiency of the associated
satellites, and develop the meaning of this "galactic conformity" effect in a
probabilistic description of the quenching of galaxies. We show that conformity
is strong, and that it varies strongly across parameter space. Several
arguments then suggest that environmental quenching and mass quenching may be
different manifestations of the same underlying process. The marked difference
in the apparent mass dependencies of environment quenching and mass quenching
which produces distinctive signatures in the mass functions of centrals and
satellites will arise naturally, since, for satellites at least, the
distributions of the environmental variables that we investigate in this work
are essentially independent of the stellar mass of the satellite.
