Constructing arithmetic subgroups of unipotent groups

2008/06/30 by Willem A. de Graaf, Willem de Graaf, Andrea Pavan +2
Mathematics · #20G15 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20G15

paper · pdf · doi:10.48550/arxiv.0806.4916

19 pages

arxiv created 2008/06/30 · openalex publication_date 2008/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G ∩ GL_m(Z). This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists.

Citations

• Arithmetic Subgroups of Algebraic Groups

Related

• Arithmetic lattices in unipotent algebraic groups
• Finite arithmetic subgroups of GL_n
• Computing in unipotent and reductive algebraic groups
• Unipotent Generators for Arithmetic Groups
• An arithmetic analog of Klein's classification of finite subgroups of SL₂(ℂ)