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arXiv · 1912.11386

On general linear groups over exchange rings

Raimund Preusser
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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 $GL_n(R)$ 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 $GL_n(R)$ that are normalised by the elementary subgroup $E_n(R)$ in the case $n\geq 3$.

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Raimund Preusser. 2019-12-23. On general linear groups over exchange rings. https://arxiv.org/abs/1912.11386

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