On general linear groups over exchange rings

Raimund Preusser

paper

On general linear groups over exchange rings

arXiv:1912.11386

Abstract

Let $R$ be an exchange ring. We prove that the relative elementary subgroups $E_{n} (R, I)$ are normal in the general linear group $G L_{n} (R)$ if $n \geq 1$ and that the standard commutator formula $E_{n} (R, I) = [E_{n} (R), E_{n} (R, I)] = [E_{n} (R), C_{n} (R, I)]$ holds if $n \geq 3$ . Moreover, we classify the subgroups of $G L_{n} (R)$ that are normalised by the elementary subgroup $E_{n} (R)$ in the case $n \geq 3$ .

arXiv admin note: text overlap with arXiv:1912.03536