Observations made with the Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (PCA) to constrain the hard X-ray emission in the NGC 5044 group are reported here. Modeling a combined PCA and ROSAT position sensitive proportional counter (PSPC) spectrum with a 0.5 - 15 keV energy range shows excess hard emission above 4 keV. Addition of a powerlaw component with spectral index of 2.6 - 2.8 and luminosity of 2.6 x10^42 ergs/s within 700 kpc in the observed energy band removes these residuals. Thus, there is a detection of a significant non-thermal component that is 32% of the total X-ray emission. Point source emission makes up at most 14% of the non-thermal emission from the NGC 5044 group. Therefore, the diffuse, point source subtracted, non-thermal component is 2.2 - 3.0x10^42 ergs/s . The cosmic-ray electron energy density is 3.6 x10^[-12] ergs cm-3 and the average magnetic field is 0.034 muGauss in the largest radio emitting region. The ratio of cosmic-ray electron energy density to magnetic field energy density, ~2.5x10^4, is significantly out of equipartition and is therefore atypical of radio lobes. In addition, the groups small size and low non-thermal energy density strongly contradicts the size-energy relationship found for radio lobes. Thus, it is unlikely to the related to the active galaxy and is most likely a relic of the merger. The energy in cosmic-rays and magnetic field is consistent with simulations of cosmic-ray acceleration by merger shocks.
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