Determination of solvable algebraic groups by dense integral subgroups

Abstract

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′.