Finite arithmetic subgroups of \(GL_ n\). III
type: Item
instance of: scholarly article
title: Finite arithmetic subgroups of \(GL_ n\). III
zbMATH Open document ID: 0805.11035
DOI: 10.1007/BF02830883
author: Yoshiyuki Kitaoka
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1994-05-05T00:00:00Z
review text: [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.
Mathematics Subject Classification ID: 11E57
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 562812
zbMATH Keywords: quadratic forms
zbMATH Keywords: finite arithmetic subgroups
zbMATH Keywords: group of rational points
zbMATH Keywords: algebraic group
reviewed by: Meinhard Peters
MaRDI profile type: Publication
cites work: Q3205428
cites work: Finite arithmetic subgroups of GLn, II
cites work: Q4271318
full work available at URL: https://doi.org/10.1007/bf02830883
OpenAlex ID: W2490841548
description: scientific article; zbMATH DE number 562812