Determination of solvable algebraic groups by dense integral subgroups

M. V. Milovanov

Belarusian State University

Abstract: 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.

UDC: 513.6

Received: 29.01.1975

 English version: Mathematical Notes, 1975, 18:5, 1019–1024

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