An example of a bireflectional spin group. (Q1423753)

Let \(\mathfrak C\) be a Cayley algebra over a field \(F\) of characteristic not \(2\) such that \(-1\) is a square in \(F\). The norm \(\mathfrak n\) of \(\mathfrak C\) is a quadratic form on \(\mathfrak C\). The author shows that the spin group \(\text{Spin}(\mathfrak C,\mathfrak n)\) is bireflectional, i.e., every element in \(\text{Spin}(\mathfrak C,\mathfrak n)\) is a product of two involutions in \(\text{Spin}(\mathfrak C,\mathfrak n)\). In the proof, the author makes use of a similar result for the special orthogonal group \(\text{O}^+(\mathfrak n)\). He also uses triality.