  It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally
characterised by an integrability condition on an
$\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where
$\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra
of $G$. The integrability condition is the vanishing of a torsion tensor of
type $(1,2)$. This is a slight improvement of an earlier result proved in
[Min-Oo M., Ruh E.A., in Differential Geometry and Complex Analysis, Springer,
Berlin, 1985, 205-211].
