  Let $H$ be a closed subgroup of a regular abelian paratopological group $G$.
The group reflexion $G^\flat$ of $G$ is the group $G$ endowed with the
strongest group topology, weaker that the original topology of $G$. We show
that the quotient $G/H$ is Hausdorff (and regular) if $H$ is closed (and
locally compact) in $G^\flat$. On the other hand, we construct an example of a
regular abelian paratopological group $G$ containing a closed discrete subgroup
$H$ such that the quotient $G/H$ is Hausdorff but not regular.
