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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) (LG), specifically  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}  are particularly strong, strong \citep[e.g.,][]{LyndenBell1974,Mateo1998,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014},  even compared to the effects on (more massive) satellite galaxies satellites  within massive groups/clusters. Specifically, the dwarf  galaxies around the Milky Way (MW) and Andromeda (M31) MW/M31  show a strikingly sharp and nearly complete  transition in their properties within $\approx 300 \kpc$, corresponding to \kpc$ (approximately  the virial radii, radius,  $\rvir$, of thehalos of the  MW and M31 for $\mvir \approx 10 ^ {12} \msun$ \citep[for example,][]{Deason2012,vanderMarel2012,BoylanKolchin2013}.  Within this distance, galaxies transition or M31), transitioning  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 \citep[e.g.,][and  references therein]{Einasto1974,McConnachie2012}. therein]{McConnachie2012}.  This environmental transition of the population is almost complete, with trend has  just a few exceptions.  Four exceptions: four  gas-rich, star-forming, irregular star-forming  galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10).  However, the LMC 10),  andSMC are likely on their first infall \citep{Besla2007,Kallivayalil2013}, and given their distances to M31, LGS 3 and IC 10 may be as well.  Furthermore,  3 - 4gas-poor,  quiescent, spheroidal gas-poor  galaxies exist reside  just beyond the halos $\rvir$  of the MW (Cetus and Tucana) and M31 (KKR 25 and possibly Andromeda XVIII), thoughthe radial velocities of  Cetus and Tucanaimply that they  likely orbited within the MW halo \citep{Teyssier2012}. The fact that almost all This trend  of the efficient  satellite galaxies within the MW/M31 halos show such strong environmental effects quenching  is particularly striking given that, because,  other than KKR 25, all known galaxies at $\mstar < 10 ^ 9 \msun$ $\mstar<10^9\msun$  that are isolated (not within $1500 \kpc$ of a more massive galaxy, and thus not strongly influenced by environmental effects) galaxy)  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}, ram-pressure stripping of extended gas around the satellite \citep[e.g.,][]{Larson1980,McCarthy2008} of the cold inter-stellar medium \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.