On the Structure of Local Orthogonal Groups

Abstract

The structure of the projective commutator subgroup of the orthogonal group is well known when isotropic lines are present. The situation is radically different in the anisotropic case where results are meager. In [3] Dieudonne gives an example of a 3-dimensional anisotropic quadratic space over a p-adic field in which the commutator subgroup Q2 of the orthogonal group contains an infinite descending chain