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\section{Introduction}  Galaxies in denser environments are more likely to have suppressed (quiescent) star-formation rates (SFR) and little-to-no cold gas than galaxies of similar stellar mass, $\mstar$, in less dense environments.  The observed environmental effects in the Local Group (LG) on the satellite dwarf galaxies within the halos of the Milky Way (MW) and Andromeda (M31) \citep[for example,][]{LyndenBell1974, Mateo1998, McConnachie2012, Phillips2014, SlaterBell2014, Spekkens2014} example,][]{LyndenBell1974,Mateo1998,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014}  are particularly strong, even compared to the effects on (more massive) satellite galaxies within massive groups/clusters. Specifically, the galaxies around the Milky Way (MW) and Andromeda (M31) show a strikingly sharp transition in their properties within $\approx 300 \kpc$, corresponding to the virial radii, $\rvir$, of the halos of the MW and M31 for $\mvir \approx 10 ^ {12} \msun$ \citep[for example,][]{Deason2012, vanderMarel2012, BoylanKolchin2013}. example,][]{Deason2012,vanderMarel2012,BoylanKolchin2013}.  Within this distance, galaxies transition from (1) having irregular to elliptical/spheroidal morphologies, (2) having most of their baryonic mass in cold atomic/molecular gas to having little-to-no measured cold gas, and (3) being actively star-forming to quiescent \citep[][and references therein]{Einasto1974, McConnachie2012}. therein]{Einasto1974,McConnachie2012}.  This environmental transition of the population is almost complete, with just a few exceptions.  Four gas-rich, star-forming, irregular galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10).  However, the LMC and SMC are likely on their first infall \citep{Besla2007, Kallivayalil2013}, \citep{Besla2007,Kallivayalil2013},  and given their distances to M31, LGS 3 and IC 10 may be as well. Furthermore, 3 - 4 gas-poor, quiescent, spheroidal galaxies exist just beyond the halos of the MW (Cetus and Tucana) and M31 (KKR 25 and possibly Andromeda XVIII), though the radial velocities of Cetus and Tucana imply that they likely orbited within the MW halo \citep{Teyssier2012}.  The fact that almost all of the satellite galaxies within the MW/M31 halos show such strong environmental effects is particularly striking given that, other than KKR 25, all known galaxies at $\mstar < 10 ^ 9 \msun$ that are isolated (not within $1500 \kpc$ of a more massive galaxy, and thus not strongly influenced by environmental effects) are actively star-forming \citep{Geha2012}.  Thus, the MW and M31 halos exert the strongest environmental influence on their galaxy populations of any observed systems, making the LG one of the most compelling laboratories to study environmental effects on galaxy evolution.  Several environmental processes within a host halo regulate the gas content, star formation, morphology, and eventual tidal 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}, tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001, DOnghia2010}, \citep[e.g.,][]{Mayer2001,DOnghia2010},  ram-pressure stripping of extended gas around the satellite \citep[e.g.,][]{Larson1980, McCarthy2008} \citep[e.g.,][]{Larson1980,McCarthy2008}  of the cold inter-stellar medium \citep[e.g.,][]{GunnGott1972, Tonnesen2009}, \citep[e.g.,][]{GunnGott1972,Tonnesen2009},  many of which can be assisted by feedback from stars and/or AGN within the satellites \citep[e.g.,][]{BaheMcCarthy2015}. In this letter, we examine the environmental quenching timescales of the current satellite galaxies in the LG, considering the possible impact of group preprocessing.