The orthogonal group over a local ring is \(4\)-reflectional
Let \(R\) be a commutative local ring such that 2 is a unit in \(R\). The author shows that every element in the orthogonal group of a free \(R\)- module of finite rank is a product of two involutions in that group. For a cyclic isometry the involutions are constructed directly. This, combined with the bireflectionality of an orthogonal group for a vector space, produces the desired result.
scientific article; zbMATH DE number 569274