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On disconnected co-regular simple groups. (English. Russian original) Zbl 0859.20041
Russ. Math. Surv. 50, No. 3, 635-637 (1995); translation from Usp. Mat. Nauk 50, No. 3, 169-170 (1995).
A group \(H\) is called a finite extension of its subgroup \(K\) if the index \([H:K]\) is finite. A reductive linear group \(G\subseteq\text{GL}(U)\) is called co-regular if the algebra \(k[U]^G\) is regular, i.e., it is generated by a system of algebraically independent elements. \(G\) is said to be quasi-co-regular if it admits a finite co-regular extension. A homomorphism \(\rho:G\to\text{GL}(V)\) is said to be co-regular (resp. quasi-co-regular) if its image is co-regular (resp. quasi-co-regular). Apart from three possible exceptions, the author gives a list of all quasi-co-regular but not co-regular connected simple linear groups, and for each such group, a list of all its co-regular finite extensions.
Reviewer: Li Fuan (Beijing)
MSC:
20G15 Linear algebraic groups over arbitrary fields
20E22 Extensions, wreath products, and other compositions of groups
20G05 Representation theory for linear algebraic groups
20E32 Simple groups
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