  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.
