Normal subgroups of the general linear groups over von Neumann regular rings

Abstract

Let A A be a von Neumann regular ring or, more generally, let A A be an associative ring with 1 whose reduction modulo its Jacobson radical is von Neumann regular. We obtain a complete description of all subgroups of G L n A , n ≥ 3 {\text {G}}{{\text {L}}_n}A,n \geq 3 , which are normalized by elementary matrices.