  In this note we give two results. First, if a latin bitrade $(T_1, T_2)$ is
primary, thin, separated, and the autotopism group of $T_1$ acts regularly on
$T_1$, then $(T_1, T_2)$ may be derived from a group-based construction.
Second, if a latin bitrade $(T_1, T_2)$ has genus 0 then the disjoint mate
$T_2$ is unique and the autotopism group of $T_1$ is equal to the autotopism
group of $T_2$.
