Geodesic
Compact homogeneous spaces of reductive Lie groups and spaces close to them
Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 342-357

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We study compact homogeneous spaces of reductive Lie groups, and also some of their analogues and generalizations (quasicompact and plesiocompact homogeneous spaces of these Lie groups). We give a description of the structure of (plesio-)uniform subgroups in reductive Lie groups. The corresponding homogeneous spaces for which the stationary subgroup has an extremal dimension (close to the minimal or maximal possible one) are described. The fundamental groups of (plesio)compact homogeneous spaces of arbitrary reductive and semisimple Lie groups are characterized. Bibliography: 16 titles.
Keywords: reductive Lie group, compact homogeneous space, lattice. 
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     title = {Compact homogeneous spaces of reductive {Lie} groups and spaces close to them},
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V. V. Gorbatsevich. Compact homogeneous spaces of reductive Lie groups and spaces close to them. Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 342-357. http://geodesic.mathdoc.fr/item/SM_2016_207_3_a2/