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Galaxies in denser environments are more likely to have suppressed (quiescent) star formation and little-to-no cold gas than galaxies of similar stellar mass, $\mstar$, in less dense environments.  The observed environmental effects within the Local Group (LG) on the satellite galaxies within the halos of the Milky Way (MW) and Andromeda (M31) are particularly strong \citep[e.g.,][]{Einasto1974, Mateo1998, McConnachie2012, Phillips2014, SlaterBell2014, Spekkens2014}, even compared to the already strong effects on (more massive) satellites within massive groups/clusters.  Specifically, the dwarf galaxies around the MW/M31 show a strikingly sharp and nearly complete transition in their properties within $\approx 300 \kpc$ (approximately the virial radius, $\rvir$, of the MW or M31), from irregular to spheroidal morphologies, from having most of their baryonic mass in cold atomic gas to having little-to-no measured cold gas, and from actively star-forming to quiescent.  This trend has just a few exceptions: 4 gas-rich, star-forming galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10), and 4 - 5 quiescent, gas-poor galaxies reside well beyond $\rvir$ of either the MW or M31 [Cetus M31: Cetus  \citep{Lewis2007}, Tucana \citep{Fraternali2009}, KKR 25 \citep{Makarov2012}, KKs 3 \citep{Karachentsev2015}, and possibly Andromeda XVIII], XVIII,  though Cetus and Tucana may have orbited within the MW halo \citep{Teyssier2012}. This efficient satellite quenching is particularly striking because, other than KKR 25 and KKs 3, at $\mstar<10^9\msun$ 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 a compelling laboratory for studying environmental processes on galaxies.