Geodesic
On non-connected simple linear groups with a~free algebra of invariants
Izvestiya. Mathematics , Tome 60 (1996) no. 4, pp. 811-856

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In this paper we study non-connected coregular (that is, with a free algebra of invariants) linear groups. A criterion for the coregularity of a semisimple group $G\subseteq \operatorname{GL}(V)$ is obtained in terms of the action of $G/G^0$ on the quotient variety $V/G^0$. A classification of connected non-coregular simple linear groups which admit a finite coregular extension is found and such extensions are described in each case. 
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     author = {D. A. Shmel'kin},
     title = {On non-connected simple linear groups with a~free algebra of invariants},
     journal = {Izvestiya. Mathematics },
     pages = {811--856},
     publisher = {mathdoc},
     volume = {60},
     number = {4},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_4_a3/}
}
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D. A. Shmel'kin. On non-connected simple linear groups with a~free algebra of invariants. Izvestiya. Mathematics , Tome 60 (1996) no. 4, pp. 811-856. http://geodesic.mathdoc.fr/item/IM2_1996_60_4_a3/