We use very high-S/N stacked spectra of $sim$29,000 nearby quiescent early-type galaxies (ETGs) from the Sloan Digital Sky Survey (SDSS) to investigate variations in their star formation histories (SFHs) with environment at fixed position along and perpendicular to the Fundamental Plane (FP). We define three classifications of local group environment based on the `identities of galaxies within their dark matter halos: central `Brightest Group Galaxies (BGGs); Satellites; and Isolateds (those `most massive in a dark matter halo with no Satellites). We find that the SFHs of quiescent ETGs are almost entirely determined by their structural parameters $sigma$ and $Delta I_e$. Any variation with local group environment at fixed structure is only slight: Satellites have the oldest stellar populations, 0.02 dex older than BGGs and 0.04 dex older than Isolateds; BGGs have the highest Fe-enrichments, 0.01 dex higher than Isolateds and 0.02 dex higher than Satellites; there are no differences in Mg-enhancement between BGGs, Isolateds, and Satellites. Our observation that, to zeroth-order, the SFHs of quiescent ETGs are fully captured by their structures places important qualitative constraints on the degree to which late-time evolutionary processes (those which occur after a galaxys initial formation and main star-forming lifetime) can alter their SFHs/structures.
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