This article is cited in 3 papers

Algorithmic questions for linear algebraic groups. I

R. A. Sarkisyan


Abstract: Let $G$ be a linear algebraic group defined over the field of rational numbers and subject to certain conditions, let $G(\mathbf R)$ be its group of real points, and let $G(\mathbf Z,m)$ be a congruence-subgroup of its group of integer points. In this paper it is proved that, using a recursive procedure, one can construct a fundamental set of $G(\mathbf Z,m)$ in $G(\mathbf R)$. This result will be applied in the second part of the article.
Bibliography: 18 titles.

UDC: 519.41

MSC: Primary 20G30, 20G35; Secondary 03F65

Received: 23.01.1979 and 29.12.1979

 English version: Mathematics of the USSR-Sbornik, 1982, 41:2, 149–179

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