Lie groups which act transitively on simply-connected compact manifolds

Let $G$ be a connected Lie group and $H$ a closed subgroup such that the homogeneous space $M=G/H$ is simply connected and compact, and such that $G$ acts locally effectively on $M$. In this paper we determine the structure of the radical of $G$. In the case that $G$ is semisimple we describe the construction of a locally effective extension $(G',H')$ of the pair $(G,H)$ for which $G$ is a maximal semisimple subgroup of $G'$.
Bibliography: 4 titles.