Finite arithmetic subgroups of \(GL_ n\). III
[For Parts I, II, cf. the author and \textit{H.-J. Bartels}, J. Reine Angew. Math. 313, 151-156 (1980; Zbl 0416.20038) and the author, Nagoya Math. J. 77, 137-143 (1980; Zbl 0435.10015).] Let \(G\) be an algebraic group in \(GL_ n (\mathbb{C})\) defined over \(\mathbb{Q}\) and \(K\) an algebraic number field with maximal order \(O_ K\). If the group \(G(O_ K)\) of rational points of \(G\) in \(M_ n(O_ K)\) is a finite group and if it satisfies a certain condition (which is satisfied e.g. when \(K\) is a nilpotent extension of \(\mathbb{Q}\) and 2 is unramified), then \(G(O_ K)\) is generated by roots of unity in \(K\) and \(G(\mathbb{Z})\). This generalizes earlier results by the author and H.-J. Bartels.
scientific article; zbMATH DE number 562812