Journal of the Australian Mathematical Society - Series A Vol. 65 Part 1 (1998) Involutions and commutators in orthogonal groups Frieder Knüppel Mathematisches Seminar Ludewig-Meyn-Straße 4 D-24098 Kiel Germany and Gerd Thomsen Abstract: Suppose we are given a regular symmetric bilinear form on a finite-dimensional vector space V over a commutative field K of characteristic $\not= 2$. We want to write given elements of the commutator subgroup $\Omega (V)$ (of the orthogonal group $\Og (V)$) and also of the kernel of the spinorial norm $\ker (\Theta )$ as (short) products of involutions and as products of commutators. PDF file size: 225K © Copyright 1998, Australian Mathematical Society