Geodesic
Lie groups which act transitively on simply-connected compact manifolds
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 558-564 
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/
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     author = {E. Ya. Vishik},
     title = {Lie groups which act transitively on simply-connected compact manifolds},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_4_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] A. M. Lukatskii, “Sfericheskie funktsii na $G$-prostranstvakh nekompaktnykh grupp Li”, Uspekhi matem. nauk, XXVI:5 (151) (1971), 212–213

[2] A. L. Onischik, “O gruppakh Li, tranzitivnykh na kompaktnykh mnogoobraziyakh”, Matem. sb., 71 (113) (1966), 483–494 | Zbl

[3] A. L. Onischik, “O gruppakh Li, tranzitivnykh na kompaktnykh mnogoobraziyakh”, Matem. sb., 75 (117) (1968), 255–263 | Zbl

[4] Shevalle, Teoriya grupp Li, t. 3, IL, Moskva, 1958