Geodesic
Rationality of the field of invariants of a triangular group
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 23-24

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Let $G$ be a connected soluble algebraic linear group over an algebraically closed field of characteristic zero. It is proved that the field of rational invariants of $G$ is a purely transcendental extension of the base field. 
@article{VMUMM_1982_2_a5,
     author = {E. B. Vinberg},
     title = {Rationality of the field of invariants of a triangular group},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {23--24},
     publisher = {mathdoc},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a5/}
}
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E. B. Vinberg. Rationality of the field of invariants of a triangular group. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 23-24. http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a5/