Geodesic
Determination of solvable algebraic groups by dense integral subgroups
Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 719-730.

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Let $G$ and $G'$ be triangularizable algebraic groups defined over the field $Q$ of rational numbers, and let $\Gamma\subset G_Q$ and $\Gamma'\subset G'_Q$ 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 Gamma and Gammaprime. 
@article{MZM_1975_18_5_a8,
     author = {M. V. Milovanov},
     title = {Determination of solvable algebraic groups by dense integral subgroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {719--730},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a8/}
}
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M. V. Milovanov. Determination of solvable algebraic groups by dense integral subgroups. Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 719-730. http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a8/