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In a recent VLBI survey of a sample of 31 Compact ($\theta \le 0\arcsecpoint 25$ at 8.4GHz), Luminous ($log L_{FIR} \ge 11.25 L_\odot$) Far Infrared Galaxies (Lonsdale, Smith and Lonsdale 1993, Ap. J. (Letters), 405, L9), we demonstrated that high--$T_b$ AGN-like radio cores are common, perhaps universal in these galaxies, comprising generally a few percent of the total 18cm radio flux density. The VLBI core characteristics do not correlate strongly with other radio, optical or infrared properties of the sample galaxies. However, we have compared the radio--infrared properties of the Luminous FIR Galaxy Sample with the properties of Radio-Quiet QSOs under the working hypotheses that: 1) The FIR luminosity of the Infrared Galaxies represents optical/UV radiation, absorbed and re-radiated by dust. 2) The observed radio emission from Radio Quiet QSOs comes from compact, high-$T_b$ cores like those found for the Luminous FIR Galaxies. Under these assumptions the Luminous FIR Galaxies and Radio-Quiet QSOs show a common, uniform correlation between UV/Optical luminosity and Radio Core luminosity. This correlation is consistent with a common energy source for the UV/Optical/Radio core luminosity in both sets of objects and suggests that the Luminous FIR Galaxies may be powered by AGN. Further implications for the origin of the emission from Luminous FIR Galaxies and possible evolutionary relationships with classical AGN will be discussed.
