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Determination of solvable algebraic groups by dense integral subgroups

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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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Literature cited

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    V. P. Platonov and M. V. Milovanov, “Determination of algebraic groups by arithmetic subgroups,” Dokl. Akad. Nauk SSSR,209, No. 1, 43–46 (1973).

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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

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  • Rational Number
  • Algebraic Group
  • Finite Index
  • Dense Subgroup
  • Birational Isomorphism