Minimal algebraic groups with finite center
type: Item
instance of: scholarly article
title: Minimal algebraic groups with finite center
zbMATH Open document ID: 0830.20068
DOI: 10.1007/BF00973477
published in: Siberian Mathematical Journal
publication date: 1994-11-08T00:00:00Z
review text: Let \(K\) be an arbitrary field. The present article is devoted to a description of those infinite connected algebraic \(K\)-groups with finite center in which any proper connected algebraic \(K\)-subgroup is finite or has infinite center. These groups will be called minimal. The minimal groups serve as models in studying abstract isomorphisms of algebraic groups. We study nonsolvable minimal \(K\)-groups. We prove the following Theorem. Let \(K\) be an arbitrary field and let \(G\) be a nonsolvable connected algebraic \(K\)-group. The group \(G\) is minimal if and only if it is a simple anisotropic \(K\)-group of semisimple rank one.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 14L40
zbMATH DE Number: 652224
zbMATH Keywords: infinite connected algebraic \(K\)-groups
zbMATH Keywords: finite center
zbMATH Keywords: connected algebraic \(K\)-subgroups
zbMATH Keywords: abstract isomorphisms of algebraic groups
author: K. N. Ponomarëv
MaRDI profile type: Publication
cites work: Q4692288
cites work: On abstract monomorphisms of \(k\)-forms of \(\text{PGL}(2)\)
cites work: Q4744461
full work available at URL: https://doi.org/10.1007/bf00973477
OpenAlex ID: W2318877537
description: scientific article; zbMATH DE number 652224