Transitive groups of similitudes generated by octonions (Q1616920)

Let \(\mathbb O\) be an alternative division algebra, of arbitrary characteristic. For several types of subspaces \(V\) of \(\mathbb O\), the authors study the structure of the group generated by the left multiplications \(\lambda_v\) with \(0\ne v \in V\), and they construct epimorphisms onto (special) orthogonal groups, like \(\mathrm{SU}_4 {\mathbb C} \to \mathrm{SO}_6 \mathbb R\) and \(\mathrm{U}_2 {\mathbb H} \to \mathrm{SO}_5 \mathbb R\).