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This efficient satellite quenching is particularly striking because, other than KKR 25, at $\mstar<10^9\msun$ \emph{all} known galaxies that are sufficiently isolated ($>1500\kpc$ from a more massive galaxy) are star-forming \citep{Geha2012, Phillips2014}.  Thus, the MW and M31 halos exert the strongest environmental influence on their satellites of any known systems, so the LG is the most compelling laboratory for studying environmental processes on galaxies.  Several environmental processes within a host halo can regulate the gas content, star formation, morphology, and eventual disruption of satellite galaxies, including gravitational tidal forces \citep[e.g.,][]{Dekel2003}, galaxy-galaxy interactions \citep[e.g.,][]{FaroukiShapiro1981} and mergers \citep[e.g.,][]{Deason2014a}, ram-pressure stripping of extended gas \citep[e.g.,][]{Larson1980,McCarthy2008} \citep[e.g.,][]{Larson1980, McCarthy2008}  or of cold inter-stellar medium \citep[e.g.,][]{GunnGott1972,Tonnesen2009}, \citep[e.g.,][]{GunnGott1972, Tonnesen2009},  some of which may be assisted by stellar feedback within the satellite \citep[e.g.,][]{BaheMcCarthy2015}. %tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010},   The key astrophysical challenge is understanding the relative importance of these processes, including which (if any) dominate, and how they might vary across both satellite and host mass scales.