Geodesic
Lie groups which act transitively on simply-connected compact manifolds
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 558-564

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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. 
@article{SM_1973_21_4_a5,
     author = {E. Ya. Vishik},
     title = {Lie groups which act transitively on simply-connected compact manifolds},
     journal = {Sbornik. Mathematics},
     pages = {558--564},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_4_a5/}
}
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E. Ya. Vishik. Lie groups which act transitively on simply-connected compact manifolds. Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 558-564. http://geodesic.mathdoc.fr/item/SM_1973_21_4_a5/