Minimal algebraic groups with finite center
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.
infinite connected algebraic \(K\)-groups
abstract isomorphisms of algebraic groups
scientific article; zbMATH DE number 652224