Let G and G′ be triangularizable algebraic groups defined over the field Q of rational numbers, and let Γ ⊂ GQ and Γ′ ⊂ G′Q be dense subgroups of them containing integral subgroups of finite index. A study is made of the conditions under which a birational isomorphism of G and G′ follows from an abstract isomorphism of Γ and Γ′.
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Translated from Matematicheskie Zametki, Vol. 18, No. 5, pp. 719–730, November, 1975.
In conclusion, I thank V. P. Platonov for his valuable discussions.
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Milovanov, M.V. Determination of solvable algebraic groups by dense integral subgroups. Mathematical Notes of the Academy of Sciences of the USSR 18, 1019–1024 (1975). https://doi.org/10.1007/BF01153570
- Rational Number
- Algebraic Group
- Finite Index
- Dense Subgroup
- Birational Isomorphism