On arithmetic subgroups of simple algebraic groups
type: Item
instance of: scholarly article
title: On arithmetic subgroups of simple algebraic groups
zbMATH Open document ID: 0594.20038
DOI: 10.1016/0024-3795(85)90145-4
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: Let k be a number field, and G an absolutely almost simple algebraic group defined over k which is either of classical type distinct from \({}^ 3D_ 4\) or \({}^ 6D_ 4\), or split, and in which every maximal k-split torus has rank at least 2. The main result of the paper is that a subgroup of G(k) is full (i.e., for each maximal k-split torus of G, every root subgroup with respect to this torus meets H nontrivially) if and only if it contains an arithmetic subgroup.
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20H05
zbMATH DE Number: 3955224
zbMATH Keywords: almost simple algebraic group
zbMATH Keywords: maximal k-split torus
zbMATH Keywords: root subgroup
zbMATH Keywords: arithmetic subgroup
author: L. N. Vaserstein
reviewed by: Arjeh M. Cohen
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90145-4
OpenAlex ID: W2044293829
cites work: ARITHMETIC PROPERTIES OF DISCRETE SUBGROUPS
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cites work: Q5648549
cites work: THE STRUCTURE OF CLASSICAL ARITHMETIC GROUPS OF RANK GREATER THAN ONE
cites work: On full subgroups in the sense of O'Meara
cites work: Q5566639
description: scientific article; zbMATH DE number 3955224