On the derived subgroups of certain unipotent subgroups of reductive groups over infinite fields
type: Item
instance of: scholarly article
title: On the derived subgroups of certain unipotent subgroups of reductive groups over infinite fields
zbMATH Open document ID: 1022.20020
author: Colin J. Bushnell
author: Guy Henniart
published in: Transformation Groups
publication date: 2003-08-04T00:00:00Z
review text: Let \(G\) be a connected reductive algebraic group defined over an infinite field \(F\). Let \(P\) be a minimal \(F\)-parabolic subgroup of \(G\), and \(N\) the unipotent radical of \(P\). The authors describe explicitly the derived group \(N_{\text{der}}\) of \(N\), and prove that \(N_{\text{der}}(F)=N(F)_{\text{der}}\), i.e., the group of \(F\)-rational points of \(N_{\text{der}}\) is just the derived group of the group \(N(F)\) of \(F\)-rational points of \(N\). This gives a simple description of the maximal Abelian quotient of the abstract group \(N(F)\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 1885649
zbMATH Keywords: connected reductive algebraic groups
zbMATH Keywords: unipotent subgroups
zbMATH Keywords: derived subgroups
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: groups of rational points
MaRDI profile type: Publication
full work available at URL: s00031-002-0011-4
OpenAlex ID: W2047974492
DOI: 10.1007/S00031-002-0011-4
description: scientific article; zbMATH DE number 1885649