Geodesic
The constructive theory of invariants
Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 359-376

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In this paper we find an explicit upper bound on the number of elements of a minimal homogeneous system of generators of the algebra of invariants of an arbitrary connected semisimple linear group over an algebraically closed field of characteristic zero. We also show that the approach to the solution of this problem proposed by Dieudonné and Carrell contains an error and does not in fact achieve its aim. Bibliography: 20 titles. 
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     author = {V. L. Popov},
     title = {The constructive theory of invariants},
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V. L. Popov. The constructive theory of invariants. Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 359-376. http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a8/