Geodesic
Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group
Izvestiya. Mathematics , Tome 7 (1973) no. 5, pp. 1039-1055.

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We find all the affine algebraic surfaces that admit a quasitransitive algebraic group of biregular automorphisms (i.e. a group such that the complement of one orbit of the action is either empty or of dimension zero). The ground field is algebraically closed and of characteristic zero. 
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V. L. Popov. Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group. Izvestiya. Mathematics , Tome 7 (1973) no. 5, pp. 1039-1055. http://geodesic.mathdoc.fr/item/IM2_1973_7_5_a3/

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