We present our discovery and analysis of dwarf galaxies in the NGC 3585 galaxy group by the KMTNet Supernova Program. Using deep stack images reaching $simeq$ 28 mag arcsec$^{-2}$ in $BVI$, we discovered 46 dwarf galaxy candidates distributed in a 7 square degree field. The dwarf galaxy candidates exhibit central surface brightness as faint as $mu_{0,V} = 26.2$ mag arcsec$^{-2}$, with effective radii larger than 150 pc and total absolute magnitudes brighter than $M_V approx -10$ mag, if at the distance of NGC 3585. The dwarf galaxy surface number density decreases with projected distance from NGC 3585. We estimate the background contamination to be about 20% based both on the number density profile and on diffuse galaxy counts in a control field. The dwarf galaxy colors and Sersic structural parameters are consistent with those found for other dwarf galaxies. Unusually, there is no indication of a change of color or brightness in the dwarf galaxy candidates with projected distance from the group center. Approximately 20% of them contain an unresolved nucleus. The nucleated fraction is larger for brighter (and redder) galaxies but is independent of distance from the group center. We identify four ultra-diffuse galaxy candidates, all near the group center. We interpret these spatial properties as suggesting that the NGC 3585 group might be dynamically younger than the typical group. The galaxy luminosity function of the NGC 3585 group has a faint-end slope of $alphaapprox -1.39$, which is roughly consistent with the slopes found for other nearby groups. The possible dependence of the slope on global group properties is still unclear, and continues to motivate our homogeneous deep survey of dozens of nearby groups.
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