Products of commutators of unipotent matrices of index $2$ in $\mathrm{GL}_n(\mathbb H)$

Abstract

The aim of this paper is to show that if $\mathbb{H}$ is the real quaternion division ring and $n$ is an integer greater than $1,$ then every matrix in the special linear group $\mathrm{SL}_n(\mathbb{H})$ can be expressed as a product of at most three commutators of unipotent matrices of index $2$.

Keywords

• Matrix decomposition
• matrix over a division ring
• commutator length

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