  We study the principal sigma-models defined on any group manifold GL x GR/GD
with breaking of GR, and their T-dual transforms. For abritary breaking we can
express the torsion and Ricci tensor of the dual model in terms of the frame
geometry of the initial principal model. Using these results, we give necessary
and sufficient conditions for the dual model to be torsionless and prove that
the one-loop renormalizability of a given principal model is inherited by its
dual partner, who shares the same beta-functions. These results are shown to
hold also if the principal model is endowed with torsion. As an application we
compute the beta-functions for the full Bianchi family and show that for some
choices of the breaking parameters the dilaton anomaly is absent: for these
choices the dual torsion vanishes. For the dualized Bianchi V model (which is
torsionless for any breaking), we take advantage of its simpler structure, to
study its two-loops renormalizability.
