Geodesic
Splittings of Lie groups and their application to the study of homogeneous spaces
Izvestiya. Mathematics , Tome 15 (1980) no. 3, pp. 441-467.

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In this paper several similar splittings of simply connected Lie groups are considered and their properties are studied. Applications of the results to the study of the structure and properties of homogeneous spaces are given. Bibliography: 17 titles. 
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V. V. Gorbatsevich. Splittings of Lie groups and their application to the study of homogeneous spaces. Izvestiya. Mathematics , Tome 15 (1980) no. 3, pp. 441-467. http://geodesic.mathdoc.fr/item/IM2_1980_15_3_a1/

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