Using new XMM and Chandra observations we present an analysis of the metal abundances of the hot gas within a radius of 100 kpc of the bright nearby galaxy group NGC 5044. Motivated by the inconsistent abundance and temperature determinations obtained by different observers for X-ray groups, we provide a detailed investigation of the systematic errors on the derived abundances considering the effects of the temperature distribution, calibration, plasma codes, bandwidth, Galactic Nh, and background rate. The iron abundance (Fe) drops from Fe ~1 solar within R ~50 kpc to Fe ~0.4 solar near R=100 kpc. This radial decline in Fe is highly significant: Fe=1.09 +/- 0.04 solar (stat) +/- 0.05 solar + 0.18 solar (sys) within R=48 kpc (5) compared to Fe=0.44 +/- 0.02 solar (stat) +/- 0.10 solar + 0.13 solar (sys) over R=48-96 kpc (5-10). The data rule out with high confidence a very sub-solar value for Fe within R=48 kpc confirming that previous claims of very sub-solar central Fe values in NGC 5044 were primarily the result of the Fe Bias: i.e., the incorrect assumption of spatially isothermal and single-phase gas when in fact temperature variations exist. Within R=48 kpc we obtain Si/Fe = 0.83 +/- 0.02 (stat) +/- 0.02 + 0.07 (sys) and S/Fe = 0.54 +/- 0.02 (stat) +/- 0.01 + 0.01 (sys) in solar units. These ratios are consistent with their values at larger radii and imply that SNIa have contributed ~80% of the iron mass within a 100 kpc radius of NGC 5044. This SNIa fraction is similar to the Sun and suggests an IMF similar to that of the Milky Way. At the very center (R ~2 kpc) the XMM and Chandra CCDs and the XMM RGS show that the Fe drops to ~50% of its value at immediately larger radius analogously to that seen in some galaxy clusters. (Abridged)
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