We present the stellar population properties of 13 dwarf galaxies residing in poor groups (low-density environment, LDE) observed with VIMOS@VLT. Ages, metallicities, and [alpha/Fe] ratios were derived from the Lick indices Hbeta, Mgb, Fe5270 and Fe5335 through comparison with our simple stellar population (SSP) models accounting for variable [alpha/Fe] ratios. For a fiducial subsample of 10 early-type dwarfs we derive median values and scatters around the medians of 5.7 pm 4.4 Gyr, -0.26 pm 0.28, and -0.04 pm 0.33 for age, log Z/Zsun, and [alpha/Fe], respectively. For a selection of bright early-type galaxies (ETGs) from the Annibali et al.2007 sample residing in comparable environment we derive median values of 9.8 pm 4.1 Gyr, 0.06 pm 0.16, and 0.18 pm 0.13 for the same stellar population parameters. It follows that dwarfs are on average younger, less metal rich, and less enhanced in the alpha-elements than giants, in agreement with the extrapolation to the low mass regime of the scaling relations derived for giant ETGs. From the total (dwarf + giant) sample we derive that age propto sigma^{0.39 pm 0.22}, Z propto sigma^{0.80 pm 0.16}, and alpha/Fe propto sigma^{0.42 pm 0.22}. We also find correlations with morphology, in the sense that the metallicity and the [alpha/Fe] ratio increase with the Sersic index n or with the bulge-to-total light fraction B/T. The presence of a strong morphology-[alpha/Fe] relation appears to be in contradiction to the possible evolution along the Hubble sequence from low B/T (low n) to high B/T (high n) galaxies. We also investigate the role played by environment comparing the properties of our LDE dwarfs with those of Coma red passive dwarfs from the literature. We find possible evidence that LDE dwarfs experienced more prolonged star formations than Coma dwarfs, however larger data samples are needed to draw more firm conclusions.
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